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<p>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.</p>

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Existence of Analytic Non-convex V-States

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Gerard Castro-López,
  • Javier Gómez-Serrano

摘要

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.