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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

STABILITY OF TWO-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS UNDER THREE-DIMENSIONAL PERTURBATIONS AND INVISCID SYMMETRY BREAKING

Texto completo
Autor(es):
Bardos, C. [1] ; Lopes Filho, M. C. [2] ; Niu, Dongjuan [3] ; Nussenzveig Lopes, H. J. [2] ; Titi, E. S. [4, 5, 6]
Número total de Autores: 5
Afiliação do(s) autor(es):
[1] Univ Paris 07, Lab J L Lions, F-75009 Paris - France
[2] Univ Fed Rio de Janeiro, Inst Matemat, Dept Matemat Aplicada, BR-21941909 Rio De Janeiro, RJ - Brazil
[3] Capital Normal Univ, Sch Math Sci, Beijing 100048 - Peoples R China
[4] Univ Calif Irvine, Dept Mech & Aerosp Engn, Dept Math, Irvine, CA 92697 - USA
[5] Weizmann Inst Sci, Dept Comp Sci & Appl Math, IL-76100 Rehovot - Israel
[6] Tech Univ Darmstadt, CSI, Darmstadt - Germany
Número total de Afiliações: 6
Tipo de documento: Artigo Científico
Fonte: SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 45, n. 3, p. 1871-1885, 2013.
Citações Web of Science: 20
Resumo

In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine both the viscous and inviscid cases. For the case of viscous flows, we prove that Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations preserve initially imposed symmetry and that such symmetric flows are stable under general three-dimensional perturbations, globally in time. We work in three different contexts: two-and-a-half-dimensional, helical, and axisymmetric flows. In the inviscid case, we observe that as a consequence of recent work by De Lellis and Szekelyhidi, there are genuinely three-dimensional weak solutions of the Euler equations with two-dimensional initial data. We also present two partial results where restrictions on the set of initial data and on the set of admissible solutions rule out spontaneous symmetry breaking; one is due to P.-L. Lions and the other is a consequence of our viscous stability result. (AU)

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