Paper Citation Record · LEDGER

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations

As of 9 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2602.22767.

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

pith.paper-citation-record.v1
2602.22767 v3

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T20:48:43.099910Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-09T07:48:35.443838Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-09T07:56:04.785377Z

Reference resolution

27 of 27 outbound references displayed

verified exact0
verified fuzzy0
unresolved27
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3d2c7e12-9d1a-4d44-9a9e-e349f77532f8 · outbound

This paper cites Stegun, editors.Handbook of mathematical functions with formulas, graphs, and mathematical tables.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Stegun, editors.Handbook of mathematical functions with formulas, graphs, and mathematical tables

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.015175Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f721ee4-d338-46f4-8af0-b4ef76f0d3d9 · outbound

This paper cites Walter de Gruyter & Co., Berlin, 1990.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Walter de Gruyter & Co., Berlin, 1990

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.104478Z

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Unavailable: canonical work link unavailable.

Observation 17831468-d130-4bd2-ad0f-2cd3cce99dcc · outbound

This paper cites Springer, Heidelberg, 2011.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Springer, Heidelberg, 2011

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.215646Z

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Observation f4e99d75-413a-43b7-8a16-fc08bf067e33 · outbound

This paper cites Bertozzi and Peter Constantin.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Bertozzi and Peter Constantin

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.253074Z

Source-reported events for the cited work

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Observation bc8c50f6-cc07-4a28-8dae-7d2ef0d35878 · outbound

This paper cites Bertozzi, John B.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Bertozzi, John B

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.310001Z

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Observation 14c698fb-eb0f-454c-8a77-393d1bf11313 · outbound

This paper cites Bertozzi, Thomas Laurent, and Flavien L´ eger.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Bertozzi, Thomas Laurent, and Flavien L´ eger

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.346128Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b37ab0a7-82a2-4794-be93-78a8bd0c50d5 · outbound

This paper cites an unresolved cited work.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.355004Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55299780-5287-4919-a95a-57a691cc8ab2 · outbound

This paper cites The regularity of the boundary of vortex patches for some nonlinear transport equations.Analysis & PDE, 16(7):1621–1650, 2023.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations The regularity of the boundary of vortex patches for some nonlinear transport equations.Analysis & PDE, 16(7):1621–1650, 2023

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.431647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d61df07-d5d2-4e6b-adfd-ae3453c43cbe · outbound

This paper cites Persistance de structures g´ eom´ etriques dans les fluides incompressibles bidimensionnels.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Persistance de structures g´ eom´ etriques dans les fluides incompressibles bidimensionnels

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.557932Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60994ed3-a7c1-469d-98ba-00597418fda2 · outbound

This paper cites An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces.Calc.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces.Calc

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.653929Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6997ddb6-f226-4a31-9df6-289cbef8cf63 · outbound

This paper cites DiPerna and Pierre-Louis Lions.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations DiPerna and Pierre-Louis Lions

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.731491Z

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Observation b4c2e396-8090-41fb-ae0b-054047a05568 · outbound

This paper cites Dritschel, Taoufik Hmidi, and Coralie Renault.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Dritschel, Taoufik Hmidi, and Coralie Renault

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.833853Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7a860c3-6322-4295-bd93-011e0bee5b6f · outbound

This paper cites Dynamic behavior of a multilayer quasigeostrophic model: weak and time-periodic solutions.Pure Appl.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Dynamic behavior of a multilayer quasigeostrophic model: weak and time-periodic solutions.Pure Appl

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:41.975976Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64761531-6faa-4312-9115-37f781284e4a · outbound

This paper cites Time quasi-periodic vortex patches for quasi-geostrophic shallow-water equations.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Time quasi-periodic vortex patches for quasi-geostrophic shallow-water equations

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.100042Z

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Observation f1735fe6-a930-4b09-b52c-44bad81e149a · outbound

This paper cites Sharp strong convergence in ideal flows.Nonlinearity, 38(12):125012, dec 2025.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Sharp strong convergence in ideal flows.Nonlinearity, 38(12):125012, dec 2025

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.167323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d45786d-de47-45a0-a7e9-1ea7a4afede8 · outbound

This paper cites Continuity of the solution map to some active scalar equations in H¨ older and Zygmund spaces.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Continuity of the solution map to some active scalar equations in H¨ older and Zygmund spaces

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.228869Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5aae49fe-6a0b-4b07-8435-149b21d2d942 · outbound

This paper cites Majda and Andrea L.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Majda and Andrea L

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.275026Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67f4a75d-076b-4e7a-8bcf-87ec6a7dcdf9 · outbound

This paper cites Extra cancellation of even Calder´ on-Zygmund operators and quasiconformal mappings.J.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Extra cancellation of even Calder´ on-Zygmund operators and quasiconformal mappings.J

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.354989Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 338fa811-579a-4528-bdc3-841618047f6a · outbound

This paper cites Continuity of the solution map of the Euler equations in H¨ older spaces and weak norm inflation in Besov spaces.Trans.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Continuity of the solution map of the Euler equations in H¨ older spaces and weak norm inflation in Besov spaces.Trans

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.417382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83b02cba-bf1c-4054-9643-0314ab6f3787 · outbound

This paper cites Dritschel.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Dritschel

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.479480Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab61eb5f-15a3-41ca-b833-b5afe94290ce · outbound

This paper cites Vortex rigid motion in quasi-geostrophic shallow-water equations.Asymptot.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Vortex rigid motion in quasi-geostrophic shallow-water equations.Asymptot

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.543121Z

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Unavailable: canonical work link unavailable.

Observation 98b03ce2-1c39-4597-b04a-a8586a37bb37 · outbound

This paper cites A revisit of patch solutions for the 2d loglog-euler type equation.arXiv preprint arXiv:2510.18759, 2025.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations A revisit of patch solutions for the 2d loglog-euler type equation.arXiv preprint arXiv:2510.18759, 2025

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.661598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e73e6744-4f07-4ded-9452-710524e3f7a3 · outbound

This paper cites Academic Press, Inc., Orlando, FL, 1986.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Academic Press, Inc., Orlando, FL, 1986

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.727570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d438ff7a-5e0d-45a3-bb09-af2a582aa900 · outbound

This paper cites Vallis.Atmospheric and oceanic fluid dynamics: fundamentals and Large-Scale Circulation.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Vallis.Atmospheric and oceanic fluid dynamics: fundamentals and Large-Scale Circulation

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.813339Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5bfc154-bbe4-4249-82a0-f5bea98c75bc · outbound

This paper cites Watson.A Treatise on the Theory of Bessel Functions.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Watson.A Treatise on the Theory of Bessel Functions

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.904808Z

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Unavailable: canonical work link unavailable.

Observation 5fa7fdcf-93d8-4720-938c-bb75d0e8144b · outbound

This paper cites Global solutions of quasi-geostrophic shallow-water fronts.J.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Global solutions of quasi-geostrophic shallow-water fronts.J

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:42.960682Z

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Unavailable: canonical work link unavailable.

Observation 23431c93-5974-46ba-804b-3fb73b88b275 · outbound

This paper cites Yudovich.

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations Yudovich

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T20:48:43.099910Z

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Pith citing papers

Observation 37a0bc56-3349-456b-bba0-a30d6964cf03 · inbound

On stationary Quasi-Geostrophic Shallow-Water flows cites this paper.

On stationary Quasi-Geostrophic Shallow-Water flows The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-07-09T07:56:04.786634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.