Nonlinear Orbital Stability for Planar Vortex Patches

Published 5 Mar 2018 in math.AP | (1803.01453v1)

Abstract: In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is proved. The proof is based on conservation of energy and vorticity, which is an analogue of the classical Liapunov function method.

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