Paper Citation Record · LEDGER

A lecture on Navier-Stokes equations

As of 11 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.18841.

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

pith.paper-citation-record.v1
2607.18841 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T14:17:52.716227Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

23 of 23 outbound references displayed

verified exact0
verified fuzzy0
unresolved23
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b57c5094-9aba-46bd-a341-700ecd9006e2 · outbound

This paper cites Wiss., vol.

A lecture on Navier-Stokes equations Wiss., vol

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.633125Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac00599c-41d1-4352-9845-56cad0221c4d · outbound

This paper cites An introduction, Grundlehren Math.

A lecture on Navier-Stokes equations An introduction, Grundlehren Math

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.637477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2da9ea4e-acd3-4cee-9fae-fcf060a50f47 · outbound

This paper cites https://perso.math.u-pem.fr/danchin.raphael/cours/coursM2-20.pdf.

A lecture on Navier-Stokes equations https://perso.math.u-pem.fr/danchin.raphael/cours/coursM2-20.pdf

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.641132Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2cbbecee-3fef-4b5e-93cb-db7336c13b32 · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.644550Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd434ecd-5bdb-46ec-8c1a-e8426d8fae71 · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.648169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d59d80ac-f2bc-4be1-8c08-63c66ceb9b60 · outbound

This paper cites Notes of a lecture series.

A lecture on Navier-Stokes equations Notes of a lecture series

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.652115Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0cac05ef-16e9-4843-8edb-03d8c3e94ca7 · outbound

This paper cites Extended abstracts of the 2023 GAP Center summer school, Ghent, Belgium, August 23 – September 2, 2023, 2024, pp.

A lecture on Navier-Stokes equations Extended abstracts of the 2023 GAP Center summer school, Ghent, Belgium, August 23 – September 2, 2023, 2024, pp

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.656791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b6d9ea5-c06d-42df-b64f-35fea343d91d · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.661421Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d720ad1-58cf-4a2b-9565-253694e5b9e8 · outbound

This paper cites Prove that (t, x)7→ et∆g (x) belongs to the spaceL2(0,∞; ˙H 1(Rn)).

A lecture on Navier-Stokes equations Prove that (t, x)7→ et∆g (x) belongs to the spaceL2(0,∞; ˙H 1(Rn))

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.665849Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7349003-7e98-44c0-a052-04656b80762c · outbound

This paper cites Exercise 21.The purpose of this exercise is to prove that mild solutions of the quadratic heat equation in dimension 5 are unique.

A lecture on Navier-Stokes equations Exercise 21.The purpose of this exercise is to prove that mild solutions of the quadratic heat equation in dimension 5 are unique

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.669854Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 426e8d3f-69b9-41af-915d-32316f60faf5 · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.673445Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e69565a-273a-4d25-8330-8f7e1e955505 · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.677971Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bafc901c-2bb1-4977-aebe-41cc463dc6e1 · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.681506Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f4ff3e0-8223-429a-a8d2-4c61f88c9eeb · outbound

This paper cites (a) Prove thata∈C b([0,∞); ˙H 1 2 (R5)).

A lecture on Navier-Stokes equations (a) Prove thata∈C b([0,∞); ˙H 1 2 (R5))

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.685398Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72ddb577-1464-445a-80c7-d6258f446372 · outbound

This paper cites Assume thatuandvbelong to Cb([0,∞); ˙H 1 2 (R5)) and satisfyu=a+B(u, u) andv=a+B(v, v).

A lecture on Navier-Stokes equations Assume thatuandvbelong to Cb([0,∞); ˙H 1 2 (R5)) and satisfyu=a+B(u, u) andv=a+B(v, v)

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.688896Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36e314ff-2cfd-4a67-b52a-5ea0e31a26a9 · outbound

This paper cites Exercise 22.As in the script, we use the notation et∆u0 =F −1 ξ ξ7→e −t|ξ|2 Fx(u0)(ξ) fort >0 andu 0 ∈ ˙H s(Rn) (s∈R).

A lecture on Navier-Stokes equations Exercise 22.As in the script, we use the notation et∆u0 =F −1 ξ ξ7→e −t|ξ|2 Fx(u0)(ξ) fort >0 andu 0 ∈ ˙H s(Rn) (s∈R)

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.692133Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 341abb93-3b60-4b0d-8ac9-4744612b6000 · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.695385Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db4289cd-8940-44a1-babb-d041e5203688 · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.699557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75fcdaad-e9bc-4a2a-a656-2334e5053df8 · outbound

This paper cites Forλ >0, denote byv λ the functionx7→v(λx).

A lecture on Navier-Stokes equations Forλ >0, denote byv λ the functionx7→v(λx)

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.702847Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8563ad97-70b2-4ac3-b941-4de4dd4eb717 · outbound

This paper cites Find α∈Rsuch thatu λ,α : (t, x)7→λ αu(λ2t, λx) is also solution of the same equation for allλ >0.

A lecture on Navier-Stokes equations Find α∈Rsuch thatu λ,α : (t, x)7→λ αu(λ2t, λx) is also solution of the same equation for allλ >0

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.706226Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2749b1d-0fd5-4231-8c67-2cf7f5d673de · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.709338Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2fb718f7-5f75-455f-af57-af53a13bd2ee · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.712822Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b338cdec-e7c1-444a-a6e1-92059e029edb · outbound

This paper cites an unresolved cited work.

A lecture on Navier-Stokes equations Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T14:17:52.716227Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.