Pith Number

pith:BKVPATX3

pith:2026:BKVPATX36E254JDR3XFIS53RHK

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On two-dimensional steady compactly supported Euler flows with constant vorticity

Changfeng Gui, Jun Wang, Wen Yang, Yong Zhang

Perturbations of annular equilibria produce both nontrivial domains and stable solutions for constant-vorticity Euler flows across three classes of overdetermined free-boundary problems.

arxiv:2602.07407 v4 · 2026-02-07 · math.AP

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Claims

C1strongest claim

For each class, we first prove a flexibility result-the existence of nontrivial admissible domains-by combining shape derivatives with local bifurcation theory. Second, we establish the corresponding rigidity results. Third, we apply the implicit function theorem to show that the standard annular flows are stable under small perturbations of the Neumann boundary condition.

C2weakest assumption

The flows are small perturbations of annular equilibria with constant vorticity, allowing the linearized operators from shape derivatives to satisfy the conditions for local bifurcation and the implicit function theorem to apply directly to the overdetermined problems.

C3one line summary

Existence, rigidity, and stability theorems are established for compactly supported steady Euler flows with constant vorticity in partially, two-phase, and fully overdetermined free-boundary problems.

Receipt and verification

First computed	2026-07-20T01:18:27.081533Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0aaaf04efbf135de2471ddca8977713ab50ac0c99e62b5e348e375af3312cc07

Aliases

arxiv: 2602.07407 · arxiv_version: 2602.07407v4 · doi: 10.48550/arxiv.2602.07407 · pith_short_12: BKVPATX36E25 · pith_short_16: BKVPATX36E254JDR · pith_short_8: BKVPATX3

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/BKVPATX36E254JDR3XFIS53RHK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0aaaf04efbf135de2471ddca8977713ab50ac0c99e62b5e348e375af3312cc07

Canonical record JSON

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    "abstract_canon_sha256": "da212d0aaab1ad80efafdcf2492e74d50160833d00dc054467e19dd3531dcccb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-02-07T06:57:57Z",
    "title_canon_sha256": "dd77008a21c890c4276092df92843e8eef7df97369a8c51189ab59a22e2e44a4"
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  "source": {
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    "kind": "arxiv",
    "version": 4
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