Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation

2024/06/14 by De Huang, Huang, De, Jiajun Tong +1 · 7 citations
Physics and Astronomy · #Solar and Space Plasma Dynamics

paper · pdf · doi:10.48550/arxiv.2406.09849

Abstract

We rigorously construct the first steady traveling wave solutions of the 2D incompressible Euler equation that take the form of a contiguous vortex-patch dipole, which can be viewed as the vortex-patch counterpart of the well-known Lamb-Chaplygin dipole. Our construction is based on a novel fixed-point approach that determines the patch boundary as the fixed point of a certain nonlinear map. Smoothness and other properties of the patch boundary are also obtained.

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