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Uniformly rotating Euler flows with compactly supported velocity

Year: 2025

Type: preprint

Abstract: For any positive integer $k$, we prove the existence of nontrivial $C^k$-smooth uniformly rotating solutions to the 2D incompressible Euler equations with compact spatial support. These solutions, which can be chosen to be small perturbations of radial flows, are the first example of smooth rotating flows with finite energy which are not locally radial. We also prove new rigidity results for rotating solutions which show that the geometric structure of these flows is severely constrained.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2511.12293

Authors: Enciso, Alberto, Fernández, Antonio J., Ruiz, David

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4416354560

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