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Paper Citation Record · LEDGER

Numerical analysis for a chemotaxis-Navier-Stokes system

As of 16 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:1908.03639.

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

pith.paper-citation-record.v1
1908.03639 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:16:43.072896Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

35 of 35 outbound references displayed

  • verified exact0
  • verified fuzzy29
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f20b76c4-de8d-42d1-9b46-502ac141f0a7 · outbound

This paper cites Amrouche and N.

Numerical analysis for a chemotaxis-Navier-Stokes system Amrouche and N

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.579708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation b2e9058e-7a8c-44aa-83ec-b7fe8852992e · outbound

This paper cites Bessemoulin-Chatard and A.

Numerical analysis for a chemotaxis-Navier-Stokes system Bessemoulin-Chatard and A

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.565963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 79f28266-1528-454d-adae-816171107966 · outbound

This paper cites Brenner and L.R.

Numerical analysis for a chemotaxis-Navier-Stokes system Brenner and L.R

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.552790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation b6ed9b1c-0569-4f28-b902-efc3dda10dce · outbound

This paper cites Chertock, K.

Numerical analysis for a chemotaxis-Navier-Stokes system Chertock, K

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.540220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.922580Z digest=sha256:117ce43f604c5faa64719d720e1e152a12478cf7f8e47e129e47ef3e17f6db0f

Observation 2d567138-c682-4e44-9ada-7ee9e374cd7b · outbound

This paper cites an unresolved cited work.

Numerical analysis for a chemotaxis-Navier-Stokes system Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:16:43.527986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 74ef9a77-2db4-4ce4-99c9-ab66c8f68f57 · outbound

This paper cites Deleuze, C.-Y.

Numerical analysis for a chemotaxis-Navier-Stokes system Deleuze, C.-Y

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.516305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.932996Z digest=sha256:79feab05bcb88d4354ec9950a6c63b1d548ffa148e30c05936ee5d4003b67f16

Observation 5bbea930-dbe2-4fc4-a4f2-1041ead0d1d1 · outbound

This paper cites Duarte-Rodr´ ıguez, L.

Numerical analysis for a chemotaxis-Navier-Stokes system Duarte-Rodr´ ıguez, L

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.504097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.938135Z digest=sha256:ceb50711f3d01d176d761caa21530a2d7db0d0fea0e38e016e50b937e5de095f

Observation ff5d6f74-5567-4b5c-a2dc-8468b66f009d · outbound

This paper cites Epshteyn and A.

Numerical analysis for a chemotaxis-Navier-Stokes system Epshteyn and A

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.489990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.945025Z digest=sha256:6120f8ecc893935806605290ba5dbd11519165734c2056873f9e5f99279a8e24

Observation 5aadc5c3-a61e-4a5a-aaa5-833c7de1afe7 · outbound

This paper cites an unresolved cited work.

Numerical analysis for a chemotaxis-Navier-Stokes system Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:16:43.475109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.949226Z digest=sha256:8e102a95332f2c82c216f1ac15077396e364cfc950348003e337e71d25b3d150

Observation e2abb966-462c-4c34-be28-be7d9e34f408 · outbound

This paper cites Filbet, A finite volume scheme for the Patlak-Keller-Segel chemotaxis model, Numer.

Numerical analysis for a chemotaxis-Navier-Stokes system Filbet, A finite volume scheme for the Patlak-Keller-Segel chemotaxis model, Numer

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.460065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.953501Z digest=sha256:4b05d1358bc17f1cc5fcf7cc067b16d5c449dc14f1aedfadb1de13374edf7fd9

Observation 70dea1fd-3325-4715-9f96-8fdad56b0387 · outbound

This paper cites Girault and P.-A.

Numerical analysis for a chemotaxis-Navier-Stokes system Girault and P.-A

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.446585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.957562Z digest=sha256:50eef3372153ee6e3bf2ca2512ebc2b7c54b1e72803a9e0736a24456ef3da4c8

Observation 0d6b71e8-eb6e-486f-a70b-702cdf692a12 · outbound

This paper cites Guill´ en-Gonz´ alez and M.

Numerical analysis for a chemotaxis-Navier-Stokes system Guill´ en-Gonz´ alez and M

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.432258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.961683Z digest=sha256:7cd1705b0e103380192f25ad57a612516ce5de8136e3ccb6e8806c286ec8305c

Observation 81fe47ac-0a3d-4c0e-bd57-f0de6733bd0d · outbound

This paper cites Guill´ en-Gonz´ alez, M.

Numerical analysis for a chemotaxis-Navier-Stokes system Guill´ en-Gonz´ alez, M

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.419786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.966106Z digest=sha256:a945711a72f756e5cd5bfe81d7ccb2597dd5d25416539ac057f72f6a0aed98af

Observation 0a1df685-ecd1-402a-b71f-92023ad64782 · outbound

This paper cites Guill´ en-Gonz´ alez, M.

Numerical analysis for a chemotaxis-Navier-Stokes system Guill´ en-Gonz´ alez, M

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.408408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.970655Z digest=sha256:9538ca2630c2ef97ec737545d3f0d015aa0dc9451ce8ae3fd155091ffdc2da16

Observation 059286e0-5c2d-4b30-9706-2749b30110c8 · outbound

This paper cites Guill´ en-Gonz´ alez, M.

Numerical analysis for a chemotaxis-Navier-Stokes system Guill´ en-Gonz´ alez, M

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.395727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.974827Z digest=sha256:a4f1ad853e0fe6164923aeb03edab2e8b0cf5d8dfc4da015eab613237ad33ce1

Observation 56ec09a6-b9ac-48cb-a8b6-afbabe346144 · outbound

This paper cites Heywood and R.

Numerical analysis for a chemotaxis-Navier-Stokes system Heywood and R

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.382319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.978865Z digest=sha256:2bd2cd421bd81baf865b2b72197dc49994abb0e87cebcb9b823a74bba580ed11

Observation 000b966f-96d2-4d77-b0ac-7ad62be9a88b · outbound

This paper cites Hill and T.

Numerical analysis for a chemotaxis-Navier-Stokes system Hill and T

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.367219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.982841Z digest=sha256:face3b50e7e0e66c983cd7d12cd4d748e98c37ba17edc68c852f87c2f66a75f3

Observation d55a0793-0929-4879-85da-e075c54017a1 · outbound

This paper cites Jiang, H.

Numerical analysis for a chemotaxis-Navier-Stokes system Jiang, H

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.352916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.986741Z digest=sha256:ae76bc121a49921b424164e930d1358de8f326f4d15fd151d8a59e675460873a

Observation 4be9395b-971c-4a52-91d2-c74aaadce403 · outbound

This paper cites Karimi and M.

Numerical analysis for a chemotaxis-Navier-Stokes system Karimi and M

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.339216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:42.990720Z digest=sha256:c3a29e4d25ed4b25468c970cadd0d4f5455bc795849bc4e49e46bb4ae9500419

Observation 4e555492-8a59-4b0b-b38f-47472517dbe1 · outbound

This paper cites Lankeit, Long-term behaviour in a chemotaxis-fluid system with logistic source, Math.

Numerical analysis for a chemotaxis-Navier-Stokes system Lankeit, Long-term behaviour in a chemotaxis-fluid system with logistic source, Math

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.324538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation f164c483-d7f7-4dba-b6ff-4adfacdf39a3 · outbound

This paper cites an unresolved cited work.

Numerical analysis for a chemotaxis-Navier-Stokes system Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:16:43.310961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation ffb576dc-9c95-4d1e-a7a8-46f4a80bb3eb · outbound

This paper cites Marrocco.

Numerical analysis for a chemotaxis-Navier-Stokes system Marrocco

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.298231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.005446Z digest=sha256:715c8bb4b6cc264b968a7b0654aae4ee6e844dc052f97cded40868785bf6cc02

Observation ae6d2824-ec7f-4dab-9620-57268bda358e · outbound

This paper cites Mizoguchi and Ph.

Numerical analysis for a chemotaxis-Navier-Stokes system Mizoguchi and Ph

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.283133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.009692Z digest=sha256:f14eb79650d96c87ffe30123cfabaaa32b4a727fbc7dc5c2191b3d29a43ef40c

Observation f99600a2-1879-44a7-b4fc-d74ade866e8c · outbound

This paper cites Necas, Les M´ ethodes Directes en Th´ eorie des Equations Elliptiques.

Numerical analysis for a chemotaxis-Navier-Stokes system Necas, Les M´ ethodes Directes en Th´ eorie des Equations Elliptiques

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.270479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.014026Z digest=sha256:116c9d7c15e5734a0753f2ac9d3e44c71763e24791b9279fc68ba92d8b2791e7

Observation 277fee8d-61f5-445f-81e9-e970168654cc · outbound

This paper cites Saito, Conservative upwind finite-element method for a simplified Keller-Segel system modelling chemotaxis, IMA J.

Numerical analysis for a chemotaxis-Navier-Stokes system Saito, Conservative upwind finite-element method for a simplified Keller-Segel system modelling chemotaxis, IMA J

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.256784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.019250Z digest=sha256:1c07217520d023a396eef8c11d0cbd3aa3d0cd18f11880e97c033edf3943a6fd

Observation f47d7e51-5662-4917-9358-90f67f8f448b · outbound

This paper cites Saito, Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis, Commun.

Numerical analysis for a chemotaxis-Navier-Stokes system Saito, Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis, Commun

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.243847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.023075Z digest=sha256:e567a274bfa6f1c78a73b65e7503bdb2b0589863629122c59f29c5ea30ee3b24

Observation 76874689-1fbc-47a2-b12d-755fd3bc69ed · outbound

This paper cites Stenberg, A technique for analysing finite element methods for viscous incompressible flow.

Numerical analysis for a chemotaxis-Navier-Stokes system Stenberg, A technique for analysing finite element methods for viscous incompressible flow

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.230731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.027202Z digest=sha256:dcc61834dd2da344c68cb5a0a87e78ee4ac0723887468323520882f898e8cf77

Observation d9c29dc6-fb31-4f46-a214-c89ec801796c · outbound

This paper cites Tao and M.

Numerical analysis for a chemotaxis-Navier-Stokes system Tao and M

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.216127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.033900Z digest=sha256:cff138941378c020848c7bd2f243b78ccfe2200a6c7f58422063d7abb4b9d1fa

Observation 40d4dcf1-b542-4e34-831d-dc21ae211c46 · outbound

This paper cites Tuval, L.

Numerical analysis for a chemotaxis-Navier-Stokes system Tuval, L

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.202067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.040398Z digest=sha256:c9834a5d57351d6228a837af8b651e536c6aca3f31f1f0c04ad2e18fb1110145

Observation b00ed3cf-e18d-4102-bae8-634fe614e74d · outbound

This paper cites an unresolved cited work.

Numerical analysis for a chemotaxis-Navier-Stokes system Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:16:43.188616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.046875Z digest=sha256:fa6e6425a7ed25105ad1c283e4ea3be198c9333fe3ef8bfdba07e832dd54ed43

Observation fcd8d632-7f36-4f2d-960f-13760c680693 · outbound

This paper cites an unresolved cited work.

Numerical analysis for a chemotaxis-Navier-Stokes system Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:16:43.174552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.051708Z digest=sha256:2d7c90abd15abc289c3dd0fad3d6a78acc75f481f83654d87b4099e943e69415

Observation 0cd6682f-30a1-420b-8284-444666c4d4e8 · outbound

This paper cites an unresolved cited work.

Numerical analysis for a chemotaxis-Navier-Stokes system Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:16:43.161527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.056494Z digest=sha256:8b4b92605eb6b16de50702213a395d7dfece2300c75a0836982216c433984222

Observation 72294fd4-9b3b-4023-98e1-9bf39bc7e767 · outbound

This paper cites Yang and Y.Chen.

Numerical analysis for a chemotaxis-Navier-Stokes system Yang and Y.Chen

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.146391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.063278Z digest=sha256:2634e935f176f249e657e4d3917f2e9396a7b4f17af4a7bf1f046b01d366a72d

Observation 3bbdd18c-0122-4d4f-aaca-37ce42ed8c0e · outbound

This paper cites Zhang and Y.

Numerical analysis for a chemotaxis-Navier-Stokes system Zhang and Y

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.129504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.068474Z digest=sha256:6fa823b3788f142e9846fd411a5390d14a7736e51f87666ddc759539878a9a09

Observation f375ab11-cc77-4fa0-aff3-66f600a961cf · outbound

This paper cites Zhang, J.

Numerical analysis for a chemotaxis-Navier-Stokes system Zhang, J

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:16:43.114545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:16:43.072896Z digest=sha256:79b33ccc9502480d73e4150e87d33e7c436e78b58c01434da04056b90c7cb593

Pith citing papers

No inbound Pith citation observations are available.