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

2017/09/21 by Cao, Daomin, Wang, Guodong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.07115

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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