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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Chipot, Michel [1] ; Droniou, Jerome [2] ; Planas, Gabriela [3] ; Robinson, James C. [4] ; Xue, Wei [1]
Total Authors: 5
Affiliation:
[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
Total Affiliations: 4
Document type: Journal article
Source: ANALYSIS AND APPLICATIONS; v. 18, n. 2, p. 211-235, MAR 2020.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 13/00048-3 - Analysis of the dynamics of rigid bodies immersed in an incompressible fluid
Grantee:Gabriela Del Valle Planas
Support type: Scholarships abroad - Research