Weak Neumann implies Stokes

Matthias Geissert, Horst Heck, Matthias Georg Hieber, Okihiro Sawada

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

Consider a domain ω ⊂ℝ n with possibly non compact but uniform C 3-boundary and assume that the Helmholtz projection P exists on L p(W) for some 1 <p <∞. It is shown that the Stokes operator in L p(W) generates an analytic semigroup on L σ p(ω) admitting maximal L q-L p-regularity. Moreover, for u 0 ε L σ p(W) there exists a unique local mild solution to the Navier-Stokes equations on domains of this form provided p > n.

Original languageEnglish
Pages (from-to)75-100
Number of pages26
JournalJournal fur die Reine und Angewandte Mathematik
Issue number669
DOIs
Publication statusPublished - 2012 Aug
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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