Nonlinear Stability for Steady Vortex Pairs

Autor(es)

Burton, Geoffrey R. ^[1] ; Nussenzveig Lopes, Helena J. ^[2] ; Lopes Filho, Milton C. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Bath, Sch Math Sci, Bath BA2 7AY, Avon - England

^[2] Univ Fed Rio de Janeiro, Inst Matemat, Ilha Fundao, BR-21941909 Rio De Janeiro, RJ - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Communications in Mathematical Physics; v. 324, n. 2, p. 445-463, DEC 2013.
• Citações Web of Science: 2

Resumo

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. (AU)

• Processo FAPESP: 06/51079-2 - Geoffrey Robert Burton | University of Bath - Inglaterra
• Beneficiário: Helena Judith Nussenzveig Lopes
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 07/51490-7 - Aspectos matemáticos da dinâmica dos fluidos incompressíveis
• Beneficiário: Milton da Costa Lopes Filho
• Modalidade de apoio: Auxílio à Pesquisa - Temático