Limits of the Stokes and Navier-Stokes equations in a punctured periodic domain

Autor(es)

Chipot, Michel ^[1] ; Droniou, Jerome ^[2] ; Planas, Gabriela ^[3] ; Robinson, James C. ^[4] ; Xue, Wei ^[1]

Afiliação do(s) autor(es)

^[1] Angew Math, Inst Math, Winterthurerstr 190, CH-8057 Zurich - Switzerland

^[2] Monash Univ, Sch Math, Clayton, Vic 3800 - Australia

^[3] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Dept Matemat, Rua Sergio Buargue de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[4] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands - England

• Tipo de documento: Artigo Científico
• Fonte: ANALYSIS AND APPLICATIONS; v. 18, n. 2, p. 211-235, MAR 2020.
• Citações Web of Science: 0

Resumo

We treat three problems on a two-dimensional ``punctured periodic domain{''}: we take Omega(r)= (-L, L)(2) \textbackslash{}rK, where r > 0 and K is the closure of an open connected set that is star-shaped with respect to 0 and has a C-1 boundary. We impose periodic boundary conditions on the boundary of Omega= (-L, L)(2), and Dirichlet boundary conditions on partial derivative(rK). In this setting we consider the Poisson equation, the Stokes equations, and the time-dependent Navier-Stokes equations, all with a fixed forcing function f, and examine the behavior of solutions as r -> 0. In all three cases we show convergence of the solutions to those of the limiting problem, i.e. the problem posed on all of Omega with periodic boundary conditions. (AU)

• Processo FAPESP: 13/00048-3 - Análise da dinâmica de corpos rígidos imersos em um fluido incompressível
• Beneficiário: Gabriela Del Valle Planas
• Modalidade de apoio: Bolsas no Exterior - Pesquisa