Nonlinear Stability of Planar Vortex Patches in an ideal fluid

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.

19 pages

References in corpus (1)

• Uniqueness of planar vortex patch in incompressible steady flow

Cited by in corpus (7)

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