Nonlinear stability of steady vortex pairs


Burton, G., Nussenzveig Lopes, H. and Lopes Filho, M. C., 2013. Nonlinear stability of steady vortex pairs. Communications in Mathematical Physics, 324 (2), pp. 445-463.

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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.


Item Type Articles
CreatorsBurton, G., Nussenzveig Lopes, H. and Lopes Filho, M. C.
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URLURL Type Full-text
DepartmentsFaculty of Science > Mathematical Sciences
Publisher Statementburtonlopes2.pdf: The original publication is available at
ID Code32407


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