Dirichlet Problem for the Stationary Navier-Stokes System on Lipschitz Domains

Hi Jun Choe, Hyunseok Kim

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We consider the stationary Navier-Stokes system on a bounded Lipschitz domain Ω in R 3 with connected boundary ∂Ω. The main concern is the solvability of the Dirichlet problem with external force and boundary data having minimal regularity. Here L q s+1/q-2(ω) denotes the standard Sobolev space with the pair (s, q) being admissible for the unique solvability in L q s+1/q (ω) of the Stokes system. We show that if 1+s≥2/q in addition, then for any and satisfying the necessary compatibility condition, there exists at least one solution in L q s+1/q (ω) + L 2 1/2 (ω) of the Dirichlet problem and this solution has a complete regularity property. The uniqueness of solutions is also shown under the smallness condition on the corresponding norms of the data.

Original languageEnglish
Pages (from-to)1919-1944
Number of pages26
JournalCommunications in Partial Differential Equations
Volume36
Issue number11
DOIs
Publication statusPublished - 2011 Nov 1

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Lipschitz Domains
Navier-Stokes System
Dirichlet Problem
Stokes System
Sobolev spaces
Unique Solvability
Compatibility Conditions
Uniqueness of Solutions
Regularity Properties
Sobolev Spaces
Solvability
Bounded Domain
Regularity
Denote
Norm
Necessary Conditions
Standards

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Dirichlet Problem for the Stationary Navier-Stokes System on Lipschitz Domains. / Choe, Hi Jun; Kim, Hyunseok.

In: Communications in Partial Differential Equations, Vol. 36, No. 11, 01.11.2011, p. 1919-1944.

Research output: Contribution to journalArticle

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