Steady double vortex patches with opposite signs in a planar ideal fluid

Daomin Cao; Guodong Wang

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arXiv · 1709.07115

Steady double vortex patches with opposite signs in a planar ideal fluid

Daomin Cao·Guodong Wang

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Abstract

In this paper we consider steady vortex flows for the incompressible Euler equations in a planar bounded domain. By solving a variational problem for the vorticity, we construct steady double vortex patches with opposite signs concentrating at a strict local minimum point of the Kirchhoff-Routh function with $k=2$. Moreover, we show that such steady solutions are in fact local maximizers of the kinetic energy among isovortical patches, which correlates stability to uniqueness.

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Daomin Cao, Guodong Wang. 2017-09-21. Steady double vortex patches with opposite signs in a planar ideal fluid. https://arxiv.org/abs/1709.07115

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