Paper Citation Record · LEDGER

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation

As of 13 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2507.10094.

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

pith.paper-citation-record.v1
2507.10094 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:47:01.545637Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

32 of 32 outbound references displayed

verified exact2
verified fuzzy19
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3b6d7e5e-1351-47a4-a278-7a89e24a82a0 · outbound

This paper cites Pure Appl.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Pure Appl

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:04.339071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ae972bec-e7e2-4999-b1bf-fe64d8a0badf · outbound

This paper cites Vasseur A., The De Giorgi method for nonlocal fluid dynamics, Nonlinear PDE Advanced Courses in Mathematics, CRM, Barcelona (2012), 1-38.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Vasseur A., The De Giorgi method for nonlocal fluid dynamics, Nonlinear PDE Advanced Courses in Mathematics, CRM, Barcelona (2012), 1-38

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:04.331919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 98f50bf5-dc87-4b2a-a82d-4acc12cdce7c · outbound

This paper cites Rational Mech.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Rational Mech

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:04.274722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 829c25b6-7161-4e7b-98e0-64864d8249d7 · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:04.185036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2a5e829d-4529-4724-a1cc-7f7e4b74dd3b · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:04.054733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 291b447e-4c66-4bda-bbb1-147c543b68a2 · outbound

This paper cites Du D., Partial r egularity of weak solutions of the Navier –Stokes equations in at the first blow -up time, Comm.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Du D., Partial r egularity of weak solutions of the Navier –Stokes equations in at the first blow -up time, Comm

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.960761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation dd6ef50b-af82-42cd-8a63-18d4261dd319 · outbound

This paper cites L., Existence and Smoothness of the Navier –Stokes Equation, Millennium Problems, Clay Math.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation L., Existence and Smoothness of the Navier –Stokes Equation, Millennium Problems, Clay Math

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.805751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f7930b2d-f8c1-425e-a2ec-eb55bf33d248 · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:03.691566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 678ab2b0-0ac7-4c86-beec-1ccf4bc47f38 · outbound

This paper cites Nachr., 4, 213-231(1951).

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Nachr., 4, 213-231(1951)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.597360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ac61a795-d713-411e-941c-e4676baf585a · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:03.590112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 585e8517-8702-4521-962c-9fec7a9bfa43 · outbound

This paper cites Discrete Contin.Dyn.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Discrete Contin.Dyn

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.581288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation aad2af8c-fe75-4c7f-aace-e203be356556 · outbound

This paper cites A., Seregin G., On partial regularity of suitable weak solutions to the threedimensional Navier–Stokes equations, J.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation A., Seregin G., On partial regularity of suitable weak solutions to the threedimensional Navier–Stokes equations, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.574742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation db3db566-a2ec-4f21-b477-091822f0b54d · outbound

This paper cites Pure Appl.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Pure Appl

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.567164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 49a00c7b-6b62-46fd-9f19-784ad9e49a86 · outbound

This paper cites On the integrability properties of Leray-Hopf solutions of the Navier-Stokes equations on $\mathbb{R}^3$.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation On the integrability properties of Leray-Hopf solutions of the Navier-Stokes equations on $\mathbb{R}^3$

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T17:46:59.892425Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a005f47d-4ed3-4466-b59a-606dc94e10e2 · outbound

This paper cites -L., Quelques methodes de resolution des problemes aux limites nonlineares, Dunod, Gauthier-Villars, Paris, (1969).

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation -L., Quelques methodes de resolution des problemes aux limites nonlineares, Dunod, Gauthier-Villars, Paris, (1969)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.560023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ab841619-fe2b-4059-9019-8e3a940f99f6 · outbound

This paper cites Math., 66 (2) (1976), 535-552.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Math., 66 (2) (1976), 535-552

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.552227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 559f7393-0cce-46df-b01a-2f016dec4bfe · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:03.545241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d3bc97f2-eb8c-4a51-a1e4-00721e105644 · outbound

This paper cites 1, 193-237 ON SMOOTHNESS AND A FINITE-TIME ”BLOWUP” 15.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation 1, 193-237 ON SMOOTHNESS AND A FINITE-TIME ”BLOWUP” 15

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.538153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a82a7a5e-0cfb-4260-b258-4a452ec41302 · outbound

This paper cites N., Remarks on the uniqueness the weak solutions to the incompressible Navier – Stokes-equations, Russian Journal of Mathematical Physics, 31, 3,(2024).

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation N., Remarks on the uniqueness the weak solutions to the incompressible Navier – Stokes-equations, Russian Journal of Mathematical Physics, 31, 3,(2024)

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.531062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 14ac24ab-bda8-4538-8216-7ef6681ecb7b · outbound

This paper cites N., Some applications of the nonlinear analysis to the differential equations, Baku, ELM, (in Russ.), (2002).

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation N., Some applications of the nonlinear analysis to the differential equations, Baku, ELM, (in Russ.), (2002)

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.523342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4e20b401-be43-4574-b3c8-0347af310339 · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T17:47:00.642399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1269bb89-9592-4476-ab0a-f95195b7a303 · outbound

This paper cites N., On semi -continuous mappings, equations and inclusions in a Banach space, Hacettepe Journal of Math and Statistics, V.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation N., On semi -continuous mappings, equations and inclusions in a Banach space, Hacettepe Journal of Math and Statistics, V

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:03.461373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5189f613-980d-4f3f-aa63-9ddcdef8102f · outbound

This paper cites N., Perturbation of the mapping and solvability theorems in Banach space, Nonlinear Analysis, (2010), doi:10.1016/j.na.2009.06.067.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation N., Perturbation of the mapping and solvability theorems in Banach space, Nonlinear Analysis, (2010), doi:10.1016/j.na.2009.06.067

Reference 24

Resolution: verified exact; doi, observed 2026-08-06T17:47:01.720840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e8607bc4-d01a-46be-95c1-7821975d37ed · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:03.223752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b429571c-6378-4fba-b746-6ebf72699975 · outbound

This paper cites N., Ahmadov M., Solvability of Equation of Prandtl -von Mises type, Theorems of Embedding.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation N., Ahmadov M., Solvability of Equation of Prandtl -von Mises type, Theorems of Embedding

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:02.961727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 63b4c702-7f60-4a92-9a0b-1fe5aec64ae6 · outbound

This paper cites N., Some embedding theorems and nonl inear differential equations.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation N., Some embedding theorems and nonl inear differential equations

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:02.750519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 23d439f5-fa5f-4f2f-80c7-8c510fe61846 · outbound

This paper cites Pure Appl.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Pure Appl

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:02.580369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8853c32b-7c97-4203-8f6d-9de046e8fb41 · outbound

This paper cites Finite time blowup for an averaged three-dimensional Navier-Stokes equation.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Finite time blowup for an averaged three-dimensional Navier-Stokes equation

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:47:01.887822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b8526f20-fd70-4f90-8102-59801f6ca529 · outbound

This paper cites Comp., in English, 3rd rev.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Comp., in English, 3rd rev

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:47:02.388646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7110ada4-9de5-4b64-8927-097cd7c5154a · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:02.320636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fa921764-ed29-4d5f-90e2-1d218aa74414 · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:02.238170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 13ff7499-05aa-4623-b452-904cf2351574 · outbound

This paper cites an unresolved cited work.

Remarks on smoothness and finite-time blowup solutions of the incompressible Navier-Stokes equation Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:47:02.052845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

No inbound Pith citation observations are available.