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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk


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

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2006, Issue 596, Pages 45–62, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2006.051, August 2006

Publication History

Received:
2004-10-20
Published Online:
2006-08-16

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 0L σ p(Ω), we prove the existence of a unique local mild solution to the Navier-Stokes problem.

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