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Paper Citation Record · LEDGER

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

As of 10 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 4 inbound Pith citation observations for arXiv:2501.07073.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.07073 v2

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:53:14.613646Z

measured 55 of 55 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:25:00.700966Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-10T09:18:32.752641Z

Reference resolution

51 of 51 outbound references displayed

  • verified exact1
  • verified fuzzy34
  • unresolved16
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 99484946-d352-4675-986e-d29968c137b5 · outbound

This paper cites Bahouri, J.-Y.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Bahouri, J.-Y

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.243995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.412791Z digest=sha256:34ecd9e366bd64de1c16faee11481e5d630bfde133af4cf993a8e6f9b0f5760e

Observation 91a7b983-6589-4b75-9435-f853f1004542 · outbound

This paper cites Biler , Singularities of solutions to chemotaxis systems , vol.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Biler , Singularities of solutions to chemotaxis systems , vol

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.226794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.417406Z digest=sha256:eef42f7d272b89008113a90da2f2eb425dbaf72f5c9b5053f9b90f5be0665681

Observation cee3ff9b-b5cb-4cb3-bb56-25426dbcb27a · outbound

This paper cites Biler, I.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Biler, I

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.212556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.421463Z digest=sha256:c19f99dc624346212780d9b8cd37e23649525510dc5378ef6999aafcc7a69b68

Observation d7466eb7-9755-45b6-b6f4-d10f61006cf3 · outbound

This paper cites Blanchet, J.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Blanchet, J

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.201040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.425557Z digest=sha256:957d0fc50188015c66bab94d319e64cc221311ad252499dc8fc0b10de9ed6199

Observation 9029aea2-8559-4e4f-b8f0-68290b980208 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:15.190196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.429636Z digest=sha256:e3783c25bd7299d9cb5f4d5c08915ec3ef1991bc30dfa7ec9fc04082d83361c0

Observation 4f3ff6b8-8230-4420-88ad-32ff0b62551a · outbound

This paper cites Existence of finite time blow-up in Keller-Segel system.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Existence of finite time blow-up in Keller-Segel system

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.434780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.434780Z digest=sha256:3dd1198fb9fd1242bc3ab48619a8586c164ab5a75e12fde869ea765b2e91c7cd

Observation c609a4b3-9dbb-4a24-ad72-8b3ace43ba1a · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:15.178832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.439683Z digest=sha256:7cd8c38e9737dfdcdb48ee39211fa9df3c35fc96f4c8066fa91d2f324d4dd1ef

Observation f49d4bcb-a9c6-4d7f-9d64-614ca44f46fb · outbound

This paper cites Collot, T.-E.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Collot, T.-E

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.168023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.443522Z digest=sha256:c2094d30a08bfcc98a51217e4037f5fabf66c37fe4e8f85d39235475bc696ecb

Observation ffab3965-5d0f-4221-a066-4cf9ffd44d9b · outbound

This paper cites PDE, 8 (2022), pp.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions PDE, 8 (2022), pp

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.156552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.447287Z digest=sha256:777d030b205f1e04c1e7f7361d140654a31c6334c30b3cfc9e77b442f37f805f

Observation 9442e68a-4721-4f62-b3d1-ccba69871c9c · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:15.145374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.451016Z digest=sha256:135326cca3b2e563b6a5dc91de5a039a4112af2a15f267f8a9fb0daafe1fdef8

Observation 12f8badb-1283-4fe2-b4cd-fa5921e0c879 · outbound

This paper cites Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.454871Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.454871Z digest=sha256:b9795574bbb4f5d6fc6ce7753822f7f58c0f71df474ead5235c11038eca2d04d

Observation 2eeafda7-8221-420f-a2a7-bae64c3277d4 · outbound

This paper cites Collot, F.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Collot, F

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.134116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.459620Z digest=sha256:9609b3ddf329f999c9a2fdbdcba6238bda1dbfafd1b1034a79fbd49a02555a93

Observation 9a3231ca-745a-478d-ad1b-9b61d34a4b01 · outbound

This paper cites Collot, P.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Collot, P

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.121284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.463402Z digest=sha256:5682189f5a1dfe52a56e2d90dbbdf913badceea72845f9ffdf33372bb1cfdc11

Observation 2278297d-fc93-46d6-b36c-838e6566f179 · outbound

This paper cites On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.467359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.467359Z digest=sha256:d3e76dfaa573e6e57e85792b32a29c3e084028fffb4725d63aed7bb28b1ae84e

Observation f13574c2-21a1-4b37-af18-5a603808c1a3 · outbound

This paper cites Corrias, B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Corrias, B

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.110113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.471801Z digest=sha256:f29d6eb16abfc16c787e9996e16252c965c297293f56d394f0b5e7630f9d7307

Observation c5699e6e-0add-4fcf-ac23-cfc7fc4be291 · outbound

This paper cites Costin, R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Costin, R

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.098567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.475693Z digest=sha256:4d8f64e0aaece04633d1b366040a1b68c3bf7179fd0ba2744cf67d72e89147fc

Observation 9f03f095-5999-43bf-94f5-2bc4d53c2047 · outbound

This paper cites Costin, R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Costin, R

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.087627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.479340Z digest=sha256:356c94ccce97d3412170e5e1d25022fcaa716350ada31b5aec9fe1f75fcd2f4a

Observation 92042c63-0f70-403d-8109-251418a5ec4c · outbound

This paper cites Demanet and W.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Demanet and W

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.076590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.482816Z digest=sha256:36ccdd652b600d5fcd0474cbc26a1fd9d8fb4239fd64ef0e7b4890c60aa7eb82

Observation 1c86bff0-1fd5-47dd-81b0-f3913cd9f11a · outbound

This paper cites Dolbeault and B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Dolbeault and B

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.065838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.485929Z digest=sha256:403621646052b6e9d21c5fb674f827f1a151af8531313cacd44010301e1ac795

Observation 966aaf0f-8473-4f6e-900f-53282fcd838e · outbound

This paper cites Donninger , Spectral theory and self-similar blowup in wave equations , Bull.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Donninger , Spectral theory and self-similar blowup in wave equations , Bull

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.054459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.489345Z digest=sha256:afa8470fbe0bbcf0c227edb35ba657547d0918529d0e9ffa725ec73cc8e2a2ad

Observation 49e87169-e856-4c8a-9fd9-0f3ef6a1b9db · outbound

This paper cites Donninger and B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Donninger and B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.041414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.492549Z digest=sha256:ba0bf98a84209daabdf88bc6e2bec914dc8f95dff142ef084a7655c3bdc8ef80

Observation 7681552c-3bc2-4b74-94be-43379e76dc92 · outbound

This paper cites Engel and R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Engel and R

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.028767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.495611Z digest=sha256:57b7b74329b353aca6617017cab75073dad58626c36ea95d753b48e066263e9f

Observation 84bd738f-36b5-48e0-befc-3df6dee85e23 · outbound

This paper cites Giga and R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Giga and R

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.015242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.498831Z digest=sha256:c840399cafdc8a12f2d847dc166a3c2cee6277e256a7bb254f29f028e3c8b07b

Observation 72de44a6-17f5-4eff-b582-b2222d369dcc · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:15.003347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.502147Z digest=sha256:2484245a40b5639bcade974266d20285c5881f185bd70070b8a6198e89371807

Observation c09a44b9-b454-4937-a6c4-01ed20ef1b2c · outbound

This paper cites Glogić and B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Glogić and B

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.990290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.505508Z digest=sha256:7a239d4dff0b07789806c8e0b0702a444f257ce521bd4ca4ffd9c1a994523ff6

Observation f49ff781-f640-4d26-9fec-86e24ff5d807 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.978553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.509005Z digest=sha256:1bace17cf390636066f21906e7e3345cd1fe3186e78125c5d0487b98f3f7545a

Observation da79da24-e577-4058-b948-5c1377f188cc · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.966784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.512317Z digest=sha256:a76343deafc185e57dc4f8c6fbe14fc8df56af966f09d4c88d2036d75622a370

Observation 841eb1d6-9024-4d7e-9e1c-bb04e0946f2f · outbound

This paper cites Horstmann , From 1970 until present: the Keller-Segel model in chemotax is and its con- sequences.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Horstmann , From 1970 until present: the Keller-Segel model in chemotax is and its con- sequences

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.954566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.516201Z digest=sha256:8133791d6663a40f7086ff11702fa6caed832099720b8e0dd8ec65da4f38e688

Observation 51463589-ae76-4b69-b638-86786104fc75 · outbound

This paper cites II, Jahresber.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions II, Jahresber

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.943574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.520045Z digest=sha256:ec146f9d1ddbb42beafb69ce9d7db8e09ca75a378f9a50f396fe5cf2017da503

Observation 007fc052-5534-442a-b3c5-09f33eb40a82 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.932997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.524243Z digest=sha256:7d7c87998472a33c040990f56b0eb8b9b669b3164bc5f72cb2a04afbd7fb6a04

Observation 9e5d4d13-5a6a-478c-a01f-2cee7474b898 · outbound

This paper cites Lenzmann , Uniqueness of ground states for pseudorelativistic Hartre e equations , Anal.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Lenzmann , Uniqueness of ground states for pseudorelativistic Hartre e equations , Anal

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.922192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.528060Z digest=sha256:76b6497a1871a32823d7c55f5a0d30efcb8ee799e09c0c9b525c749f850977b5

Observation acdd27d9-29e1-4253-8e01-d8ec4405b358 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.910455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.532038Z digest=sha256:d4272bcc32b9ac0c64268cd78c0edbe863c961d8b0138a3118b8def9de4781a8

Observation 2cc1d38d-5e63-4a10-ac6a-d59e266a6a4b · outbound

This paper cites Pure Appl.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Pure Appl

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.898169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.535904Z digest=sha256:3ec8b7c30e101385a9221e58e1e6def657c10fccfa596fc86d1a1d4893f7330a

Observation 1160a233-c180-4eed-b393-3ce047d9f8de · outbound

This paper cites Li , Mode stability for self-similar blowup of L2 slightly supercritical NLS , in preparation.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Li , Mode stability for self-similar blowup of L2 slightly supercritical NLS , in preparation

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.887369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.540173Z digest=sha256:ac04bc81122025d1a344f108de5bb1f43bfcd5ee8a5c79c5e801daca9e02ef0f

Observation 11d09e64-c0f8-4d7e-9dc0-d65faed9071c · outbound

This paper cites On stability of self-similar blowup for mass supercritical NLS.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions On stability of self-similar blowup for mass supercritical NLS

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.544074Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.544074Z digest=sha256:57588e080d37a4053b8ebec05fc457cdcb3c020dc060a93f02d8912349e50fb6

Observation c2caca7d-61ec-4d4a-b347-f0153c935990 · outbound

This paper cites Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensions.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensions

Reference 37

Resolution
verified exact
local_arxiv, observed 2026-08-10T20:53:14.669019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.548549Z digest=sha256:29a495324aae77e368b1506ea6c3abf5d8df2a282483872c3345cc52bcabe23e

Observation d0948709-f8d7-4131-bc74-0b9714ff851e · outbound

This paper cites Merle, P.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Merle, P

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.876320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.553072Z digest=sha256:ad2d3f52ebc0f25b18bfea1a33b69533daa785315cd12828c62c05d4d5ecc35f

Observation e7b91d63-4e6e-4790-8b8c-30941eb3a4df · outbound

This paper cites Nagai , Blow-up of radially symmetric solutions to a chemotaxis sys tem, Adv.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Nagai , Blow-up of radially symmetric solutions to a chemotaxis sys tem, Adv

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.866162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.557106Z digest=sha256:0c541a417c0bfa04cb0e98ef245cf73462b49eaa25bf47d0e9239c210d77c693

Observation 742ea09c-7547-4332-b8ca-09b17f39bd78 · outbound

This paper cites Korean Math.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Korean Math

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.855010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.561186Z digest=sha256:c53584d68fb3637a1115155064d17ceda702e67f47fd491c894d085b8debae62

Observation e535cbf9-f0c1-48cf-ac80-f03b1ec9b9d4 · outbound

This paper cites Naito and T.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Naito and T

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.844914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.564993Z digest=sha256:048fc3bd59b76ecb6d397c269df29c922110c6defbd5f560b65774dfa9357587

Observation de800116-643b-41df-b666-c81bcdba3650 · outbound

This paper cites Nakanishi and W.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Nakanishi and W

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.832765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.568987Z digest=sha256:66ae60421334511a6cc9b83121722dd8d2627747667b0f9f50f6c7220b66d379

Observation 795def4c-500c-412d-a522-01aec288e58c · outbound

This paper cites Construction of type I-Log blowup for the Keller-Segel system in dimensions $3$ and $4$.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Construction of type I-Log blowup for the Keller-Segel system in dimensions $3$ and $4$

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.574234Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.574234Z digest=sha256:f41c0d050c17501f1388c8bee5954b9a44bf876de3c30cae21a5d97631f440ef

Observation 0396e611-2c2f-499e-b5ed-7228315d2d8c · outbound

This paper cites Oga w a and H.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Oga w a and H

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.821393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.578842Z digest=sha256:7dc36be5fe52a863cab949604c54a3ea4da44f99dc2f0d76e8b878bbe89526f5

Observation 4e49233d-4737-475c-9086-63bd236ad656 · outbound

This paper cites Perelman , On the formation of singularities in solutions of the critic al nonlinear Schrödinger equation, Ann.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Perelman , On the formation of singularities in solutions of the critic al nonlinear Schrödinger equation, Ann

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.810148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.583081Z digest=sha256:659e98c5529588d0df2defa1014132d223091ad1a44434a83144d7def1712b90

Observation 8274089a-f64f-47c3-a618-e398395b4413 · outbound

This paper cites Raphaël and R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Raphaël and R

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.798929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.587264Z digest=sha256:7f675b1fc2ceb25fc9cc67e849acbde517a0aafa9c0a436ca42bba2e8e3f71e0

Observation ea517f9c-ba30-4f0b-bc3d-aaff31d7e5e0 · outbound

This paper cites Reed and B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Reed and B

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.787119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.591400Z digest=sha256:a8f87808130a2a2c4ef7004574552c5074167c5e28b1c2884f0d03b50977aa0b

Observation ccc1c31e-0191-43de-b7a1-83d1bbdf9cd5 · outbound

This paper cites Simon , Harmonic analysis.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Simon , Harmonic analysis

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.774751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.595519Z digest=sha256:c0982fcb4904c33b7834be9c5972d21c5208b1b4ad6af60e8afc86e2dbb742c8

Observation 542e915d-fc55-49d5-bbe7-6dcbb75d2aa9 · outbound

This paper cites Souplet and M.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Souplet and M

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.763227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.599618Z digest=sha256:2b475ea200dbe3a7ff7d382f357ac9db0578a55101e8070ebc605d462cd18987

Observation 129faebb-5f2a-4ce4-9244-f78ea3f3bd0f · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.751418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.603892Z digest=sha256:25c433541cab49931c09e7b4f16d31dfcf85a36bc78bca16231f95b37cc0272c

Observation c0b93c86-1b89-4eda-a4ab-7420b63b074b · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.738021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.609224Z digest=sha256:fd1367e847734a652d05141ef5213c327f8b84bff630e54c4c5b7763bd05b168

Observation 47d26cf9-767b-4223-87aa-fac166777d07 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.726177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T20:53:14.613646Z digest=sha256:1e91a05350aeba72d537ce410fbb6ad84ca138199ff75d1faf6631548c0ed665

Pith citing papers

Observation 9afe58b9-d730-49da-95dd-5695727b4078 · inbound

Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum cites this paper.

Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 32

Resolution
unresolved
no resolver link, observed 2026-08-06T17:25:00.700966Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T17:25:00.700966Z digest=sha256:5a039603a4d765f1e3ab201fbc2c3ff1c4c7f6ad2af3a4dc61f4b642af87eb2d

Observation 18af0467-5150-460b-8426-b1ff14469bb3 · inbound

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system cites this paper.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 62

Resolution
unresolved
no resolver link, observed 2026-08-05T21:48:41.642972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T21:48:41.642972Z digest=sha256:3597e452b689628fecb55d0e8a97801be9540dee8320434e241f724fba47f019

Observation 5a5d66f6-da47-40bd-8818-4b1dd595dfe0 · inbound

Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches cites this paper.

Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 214

Resolution
verified exact
arxiv_id, observed 2026-05-10T09:18:32.755448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-05-10T07:13:10.140500Z digest=sha256:a578a2e3516467e4c54057db8fb4ad47611b03043eae212dad743923f3972469

Observation d42bc6b1-7fc7-4b21-ae14-ac2538833a9f · inbound

Finite time blow-up for an inhomogeneous parabolic equation cites this paper.

Finite time blow-up for an inhomogeneous parabolic equation Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 25

Resolution
unresolved
no resolver link, observed 2026-07-14T06:33:18.586775Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-14T06:33:18.586775Z digest=sha256:81864e96e6b5be5dd141d8de936d8dda997e5e1351aed91b31e1743ae4c7046d