Nonlinear orbital stability for planar vortex patches

Cao, Daomin; Wan, Jie; Wang, Guodong

doi:10.1090/proc/14077

Nonlinear orbital stability for planar vortex patches
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by Daomin Cao, Jie Wan and Guodong Wang PDF

Proc. Amer. Math. Soc. 147 (2019), 775-784 Request permission

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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