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

Hi Jun Choe, Hyunseok Kim

Research output: Contribution to journalArticle

13 Citations (Scopus)


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
Issue number11
Publication statusPublished - 2011 Nov 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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