Nonlinear stability of steady vortex pairs

Reference:

Burton, G., Nussenzveig Lopes, H. and Lopes Jr, M., 2013. Forthcoming. Nonlinear stability of steady vortex pairs. Communications in Mathematical Physics

Related documents:

Related URLs:

• http://arxiv.org/abs/1206.5329

Abstract

In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.

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