Incompressible Flow Around a Small Obstacle and the Vanishing Viscosity Limit

Autor(es)

Iftimie, Dragos ^[1] ; Lopes Filho, Milton C. ^[2] ; Nussenzveig Lopes, Helena J. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Lyon 1, Inst Camille Jordan, CNRS, UMR 5208, F-69622 Villeurbanne - France

^[2] Univ Estadual Campinas, IMECC, Dept Matemat, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Communications in Mathematical Physics; v. 287, n. 1, p. 99-115, APR 2009.
• Citações Web of Science: 10

Resumo

In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior domain converge to solutions of the Euler system in the full space when both viscosity and the size of the obstacle vanish. We prove that this convergence is true assuming two hypotheses: first, that the initial exterior domain velocity converges strongly in L (2) to the full-space initial velocity and second, that the diameter of the obstacle is smaller than a suitable constant times viscosity, or, in other words, that the obstacle is sufficiently small. The convergence holds as long as the solution to the limit problem is known to exist and stays sufficiently smooth. This work complements the study of incompressible flow around small obstacles, which has been carried out in {[}4-6]. (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
• Processo FAPESP: 06/04861-7 - An illustration of boundary layer behavior with circularly symmetric flows
• Beneficiário: Helena Judith Nussenzveig Lopes
• Modalidade de apoio: Auxílio à Pesquisa - Reunião - Exterior