Mixed boundary value problems for the stokes system

R. Brown, I. Mitrea, M. Mitrea, M. Wright

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

We prove the well-posedness of the mixed problem for the Stokes system in a class of Lipschitz domains in ℝn, n ≥ 3. The strategy is to reduce the original problem to a boundary integral equation, and we establish certain new Rellich-type estimates which imply that the intervening boundary integral operator is semi-Fredholm. We then prove that its index is zero by performing a homotopic deformation of it onto an operator related to the Lamesystem, which has recently been shown to be invertible.

Original languageEnglish
Pages (from-to)1211-1230
Number of pages20
JournalTransactions of the American Mathematical Society
Volume362
Issue number3
DOIs
StatePublished - Mar 2010

Keywords

  • Layer potentials
  • Lipschitz domains
  • Mixed boundary value problems
  • Stokes system
  • Well-posedness

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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