Nonlinear Orbital Stability for Planar Vortex Patches
Daomin Cao, Guodong Wang, Jie Wan
TL;DR
This paper proves the nonlinear orbital stability of steady vortex patches in a planar domain by leveraging energy and vorticity conservation, extending classical stability results to a broader class of vortex configurations.
Contribution
It introduces a novel proof of nonlinear stability for vortex patches that maximize kinetic energy, using energy and vorticity conservation principles.
Findings
Nonlinear orbital stability of steady vortex patches established.
Stability proof based on energy and vorticity conservation.
Results apply to isolated vortex patches in bounded domains.
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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Taxonomy
TopicsNavier-Stokes equation solutions · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering