Weak Neumann implies Stokes

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

Research output: Contribution to journal › Article

20 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

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Hermann Von Helmholtz
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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Weak Neumann implies Stokes. / Geissert, Matthias; Heck, Horst; Hieber, Matthias Georg; Sawada, Okihiro.

In: Journal fur die Reine und Angewandte Mathematik, No. 669, 08.2012, p. 75-100.

Research output: Contribution to journal › Article

Geissert, M, Heck, H, Hieber, MG & Sawada, O 2012, 'Weak Neumann implies Stokes', Journal fur die Reine und Angewandte Mathematik, no. 669, pp. 75-100. https://doi.org/10.1515/CRELLE.2011.150
Geissert M, Heck H, Hieber MG, Sawada O. Weak Neumann implies Stokes. Journal fur die Reine und Angewandte Mathematik. 2012 Aug;(669):75-100. https://doi.org/10.1515/CRELLE.2011.150
Geissert, Matthias ; Heck, Horst ; Hieber, Matthias Georg ; Sawada, Okihiro. / Weak Neumann implies Stokes. In: Journal fur die Reine und Angewandte Mathematik. 2012 ; No. 669. pp. 75-100.
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