L p-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Matthias Geissert, Horst Heck, Matthias Georg Hieber

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Abstract

Consider the equations of Navier-Stokes in the exterior of a rotating domain. It is shown that, after rewriting the problem on a fixed domain Ω, the solution of the corresponding Stokes equation is governed by a C 0-semigroup on L σ p(Ω), 1 <p <∞, with generator . Moreover, for and initial data u 0 ∈ L σ p(Ω), we prove the existence of a unique local mild solution to the Navier-Stokes problem.

Original languageEnglish
Pages (from-to)45-62
Number of pages18
JournalJournal fur die Reine und Angewandte Mathematik
Issue number596
DOIs
Publication statusPublished - 2006 Jul 1
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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