Nonlinear Stability of Planar Vortex Patches in an ideal fluid

2017/06/30 by Cao, Daomin, Wang, Guodong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.10070

Abstract

In this paper, we prove nonlinear stability of planar vortex patches concentrated near an isolated minimum point of the Robin function in a general bounded domain. These vortex patches are stationary solutions of the two-dimensinal incompressible Euler equations. The result is obtained by showing that these concentrated vortex patches are in fact isolated maximizers of the kinetic energy among isovortical patches.

Related

• Steady double vortex patches with opposite signs in a planar ideal fluid
• Nonlinear Orbital Stability for Planar Vortex Patches
• Stability in L¹ of circular vortex patches
• Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability
• Steady vortex patches near a rotating flow with constant vorticity in a planar bounded domain