Paper Citation Record · LEDGER

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc

As of 12 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 2 inbound Pith citation observations for arXiv:2412.05973.

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

pith.paper-citation-record.v1
2412.05973 v2

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T20:22:30.463500Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:46:52.494062Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-09T07:56:04.764359Z

Reference resolution

44 of 44 outbound references displayed

verified exact0
verified fuzzy31
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 626aeca1-208f-46e3-b837-e0d944feb933 · outbound

This paper cites Brock and P.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Brock and P

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T20:22:30.250919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bbef796-b547-416e-a132-a769565e3c16 · outbound

This paper cites Continuous Steiner-symmetrization.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Continuous Steiner-symmetrization

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.193563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ab5f8d51-e243-4153-9cbe-28e1fdf2c137 · outbound

This paper cites Continuous rearrangement and symmetry o f solutions of elliptic problems.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Continuous rearrangement and symmetry o f solutions of elliptic problems

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.174813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e8ea6090-b98f-4a1f-9731-50e34894c670 · outbound

This paper cites Rearrangements and applications to symmet ry problems in PDE.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Rearrangements and applications to symmet ry problems in PDE

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.154271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0c4f1f6d-0e71-4ad0-a567-a591a2c56071 · outbound

This paper cites Symmetry for a general class of overdeter mined elliptic problems.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Symmetry for a general class of overdeter mined elliptic problems

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.137456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 36216bea-d227-4731-867a-c8dd25af6ac7 · outbound

This paper cites Motions of vortex patches.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Motions of vortex patches

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.116979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation be01b58f-8364-4cb9-bc23-4f9aa32ef734 · outbound

This paper cites an unresolved cited work.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T20:22:31.103224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c5d40c5a-9f57-4214-aab3-15ac8b7e80ab · outbound

This paper cites Rotating vortex patches for the planar Euler equations in a disk.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Rotating vortex patches for the planar Euler equations in a disk

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.085821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0d370994-15b3-4b2e-b5cf-b2f50a8f73fd · outbound

This paper cites U niformly rotating smooth solutions for the incompressible 2D Euler equations.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc U niformly rotating smooth solutions for the incompressible 2D Euler equations

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.070698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 74aa91eb-ebea-4a2e-a734-b1ab95d01cbf · outbound

This paper cites An analytical and numerical study of steady patches in the disc.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc An analytical and numerical study of steady patches in the disc

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.047710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6ccabd8b-bdfd-4bf9-ae15-87c41fca82ed · outbound

This paper cites Doubly connected V -states for the planar Euler equations.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Doubly connected V -states for the planar Euler equations

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.029942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e427eed4-82ef-47d3-8418-6942b14a4eb0 · outbound

This paper cites v-s tates.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc v-s tates

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:31.016046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0f8f5bc3-b0aa-4ed2-af13-b46aa84252b2 · outbound

This paper cites Smooth nonradial stationary Euler flows on the plane with compact support.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Smooth nonradial stationary Euler flows on the plane with compact support

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T20:22:30.321446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b04b9583-121e-41dc-96e8-3bb69107846d · outbound

This paper cites A Schiffer-type problem for annuli with applications to stationary planar Euler flows.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc A Schiffer-type problem for annuli with applications to stationary planar Euler flows

Reference 14

Resolution: metadata mismatch; local_arxiv, observed 2026-08-11T20:22:30.550850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0acb5491-2df3-473d-b4d3-19072a6dc06d · outbound

This paper cites an unresolved cited work.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-11T20:22:31.002652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f3225f51-965b-4b84-af6b-9c8f98188cd1 · outbound

This paper cites Vortex patches choreography for active scalar equations.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Vortex patches choreography for active scalar equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.989384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5793b5f1-388d-44ad-86f5-6bea8e672c19 · outbound

This paper cites Non uniform rotating vortices and periodic orbits for the two-dimensional Euler equations.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Non uniform rotating vortices and periodic orbits for the two-dimensional Euler equations

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.974773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 898d4c1b-7841-4d46-8f1b-77f10ffdcd2c · outbound

This paper cites Existence of non-trivial non-concentrated compactly supported stationary solutions of the 2d euler equation with ﬁnite e nergy.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Existence of non-trivial non-concentrated compactly supported stationary solutions of the 2d euler equation with ﬁnite e nergy

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.955001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3d725bf6-0f7f-46df-b39a-19d051285103 · outbound

This paper cites Sym metry in stationary and uniformly rotating solutions of active scalar equations.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Sym metry in stationary and uniformly rotating solutions of active scalar equations

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.936726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5c843072-a007-4344-a182-93eea68e9bb6 · outbound

This paper cites On a classification of steady solutions to two-dimensional Euler equations.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc On a classification of steady solutions to two-dimensional Euler equations

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T20:22:30.358363Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06c07b69-098d-470c-b603-0409bf5fe76e · outbound

This paper cites Hamel and A.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Hamel and A

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.917229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8a9c0c8e-7492-4901-8d2f-d923cd55cbf0 · outbound

This paper cites A Liouville theorem for th e Euler equations in the plane.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc A Liouville theorem for th e Euler equations in the plane

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.901599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fdd88431-be16-44e0-b2ee-00e6e36528c1 · outbound

This paper cites Circular ﬂows for the Eu ler equations in two-dimensional annular domains, and related free boundary problems.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Circular ﬂows for the Eu ler equations in two-dimensional annular domains, and related free boundary problems

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.884538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e02bb023-44f4-43f2-b11d-3e24b5d7db37 · outbound

This paper cites an unresolved cited work.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-11T20:22:30.868769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1d2ed66c-ad02-48c5-8a27-80850da07b83 · outbound

This paper cites an unresolved cited work.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-11T20:22:30.853878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f65dfd4c-5b9d-4018-850f-cd1f22450a62 · outbound

This paper cites On the trivial solutions for the rotating patch mod el.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc On the trivial solutions for the rotating patch mod el

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.829354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2861c660-3871-4087-bf8f-f6d8d9a575e8 · outbound

This paper cites Degenerate bifurcation of the r otating patches.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Degenerate bifurcation of the r otating patches

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.814990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 22a49c04-978d-4ed2-8b5c-0f0a577bbe53 · outbound

This paper cites Existence of corotating and cou nter-rotating vortex pairs for active scalar equations.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Existence of corotating and cou nter-rotating vortex pairs for active scalar equations

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.791243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation db336ef5-4085-4335-bc8f-7a88a9b8cb59 · outbound

This paper cites Boundary regula rity of rotating vortex patches.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Boundary regula rity of rotating vortex patches

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.774853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 41d13f7d-9b42-47d9-9b8f-ad34690aacb9 · outbound

This paper cites Rearrangements and convexity of level sets in PDE , volume 1150 of Lecture Notes in Mathematics.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Rearrangements and convexity of level sets in PDE , volume 1150 of Lecture Notes in Mathematics

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.761058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fb0b5732-53cb-4e35-9a0e-ebc8d5df13ec · outbound

This paper cites an unresolved cited work.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-11T20:22:30.747293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ce4201be-02e1-4a84-be94-830744adf9ca · outbound

This paper cites Lieb and Michael Loss.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Lieb and Michael Loss

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.733530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 06c80a19-d388-4c01-a40d-f2a1062a74f0 · outbound

This paper cites An overdetermined problem in Riesz-p otential and fractional Laplacian.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc An overdetermined problem in Riesz-p otential and fractional Laplacian

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.718637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a71fe750-90b9-4d99-a70e-6edcf419d2dd · outbound

This paper cites 2D homogeneous solutions to the Euler equation.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc 2D homogeneous solutions to the Euler equation

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.705755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 09644ca0-a014-40fe-915b-10103de0e192 · outbound

This paper cites Addendum: 2D homogeneous solu tions to the Euler equation [ MR3359160].

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Addendum: 2D homogeneous solu tions to the Euler equation [ MR3359160]

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.690686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2ea8b647-dbfc-42a8-84da-b9a8fffdfb5a · outbound

This paper cites Majda and Andrea L.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Majda and Andrea L

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.677321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c3f64bf0-67e3-4d8d-b1d3-f6bd122ac070 · outbound

This paper cites Space-ﬁlling curves.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Space-ﬁlling curves

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.663889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 09ed52a7-bef7-4156-9b49-d5182c0833b1 · outbound

This paper cites A symmetry problem in potential theory.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc A symmetry problem in potential theory

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.646201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6143ddfe-7529-4496-960f-15b546e76b32 · outbound

This paper cites an unresolved cited work.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-11T20:22:30.630515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0815ced7-00f8-4748-99b4-29b2f8f5c4ce · outbound

This paper cites Corotating steady vortex ﬂows with N -fold symmetry.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Corotating steady vortex ﬂows with N -fold symmetry

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.614833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f80deb65-6c8f-4f2e-920c-3121f1d1c861 · outbound

This paper cites On radial symmetry of rotating vo rtex patches in the disk.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc On radial symmetry of rotating vo rtex patches in the disk

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:22:30.600648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ddb3610a-8423-4f70-aa32-c03c0f5695b4 · outbound

This paper cites Degenerate bifurcations of two-fold doubly-connected uniformly rotating vortex patches.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Degenerate bifurcations of two-fold doubly-connected uniformly rotating vortex patches

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-11T20:22:30.455222Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7e4751b-8e79-452a-8622-4a81a4dcf3d6 · outbound

This paper cites On the rigidity of the 2D incompressible Euler equations.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc On the rigidity of the 2D incompressible Euler equations

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-11T20:22:30.459190Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd7de879-7739-4f68-9780-7a1b48b2ee94 · outbound

This paper cites an unresolved cited work.

Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-11T20:22:30.585751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 3224ef73-c6db-4684-ba69-6ee0f206a909 · inbound

Remarks on radial symmetry of stationary and uniformly-rotating solutions for the 2D Euler equation cites this paper.

Remarks on radial symmetry of stationary and uniformly-rotating solutions for the 2D Euler equation Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T10:46:52.494062Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e1c588c-508e-4df7-a0cd-d813378975a3 · inbound

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

On stationary Quasi-Geostrophic Shallow-Water flows Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-07-09T07:56:04.765507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.