Existence of analytic non-convex V-states

2024/11/20 by Gerard Castro-López, Javier Gómez-Serrano, Castro-López, Gerard +1 · 1 citation
Computer Science · #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2411.12958

Abstract

V-states are uniformly rotating vortex patches of the incompressible 2D Euler equation and the only known explicit examples are circles and ellipses. In this paper, we prove the existence of non-convex V-states with analytic boundary which are far from the known examples. To prove it, we use a combination of analysis of the linearized operator at an approximate solution and computer-assisted proof techniques.

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• Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity

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