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Limits of the Stokes and Navier-Stokes equations in a punctured periodic domain
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Chipot, Michel, Droniou, Jerome, Planas, Gabriela, Robinson, James C. and Xue, Wei (2020) Limits of the Stokes and Navier-Stokes equations in a punctured periodic domain. Analysis and Applications, 18 (2). pp. 211-235. doi:10.1142/S0219530519500118 ISSN 0219-5305.
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WRAP-limits-Stokes-Navier-Stokes-equations-punctured-periodic-domain-Robinson-2019.pdf - Accepted Version - Requires a PDF viewer. Download (638Kb) | Preview |
Official URL: https://doi.org/10.1142/S0219530519500118
Abstract
We treat three problems on a two-dimensional “punctured periodic domain”: we take Ωr=(−L,L)2∖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 C1 boundary. We impose periodic boundary conditions on the boundary of Ω=(−L,L)2, and Dirichlet boundary conditions on ∂(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 Ω with periodic boundary conditions.
Item Type: | Journal Article | ||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Navier-Stokes equations, Boundary value problems, Fluid mechanics -- Mathematical models | ||||||||||||||||||
Journal or Publication Title: | Analysis and Applications | ||||||||||||||||||
Publisher: | World Scientific Publishing | ||||||||||||||||||
ISSN: | 0219-5305 | ||||||||||||||||||
Official Date: | March 2020 | ||||||||||||||||||
Dates: |
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Volume: | 18 | ||||||||||||||||||
Number: | 2 | ||||||||||||||||||
Page Range: | pp. 211-235 | ||||||||||||||||||
DOI: | 10.1142/S0219530519500118 | ||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||
Reuse Statement (publisher, data, author rights): | Electronic version of an article published as Analysis and Applications, Volume, Issue, 2019 Pages] https://doi.org/10.1142/S0219530519500118] © [copyright World Scientific Publishing Company] https://www.worldscientific.com/worldscinet/aa | ||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||
Date of first compliant deposit: | 1 July 2019 | ||||||||||||||||||
Date of first compliant Open Access: | 29 July 2020 | ||||||||||||||||||
RIOXX Funder/Project Grant: |
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