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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Strong $ L^p$-solutions to the Navier-Stokes flow past moving obstacles: The case of several obstacles and time dependent velocity


Authors: Eva Dintelmann, Matthias Geissert and Matthias Hieber
Journal: Trans. Amer. Math. Soc. 361 (2009), 653-669
MSC (2000): Primary 76D03, 35Q30, 35B30
Published electronically: September 26, 2008
MathSciNet review: 2452819
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Abstract: Consider the Navier-Stokes flow past several moving or rotating obstacles with possible time-dependent velocity. It is shown that under suitable assumptions on the data, there exists a unique, local strong solution in the $ L^p-L^q$-setting for suitable $ p,q \in (1,\infty)$. Moreover, it is proved that this strong solution coincides with the known mild solution in the very weak sense.


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Additional Information

Eva Dintelmann
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, D-64289 Darmstadt, Germany
Email: dintelmann@mathematik.tu-darmstadt.de

Matthias Geissert
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, D-64289 Darmstadt, Germany
Email: geissert@mathematik.tu-darmstadt.de

Matthias Hieber
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, D-64289 Darmstadt, Germany
Email: hieber@mathematik.tu-darmstadt.de

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04684-9
PII: S 0002-9947(08)04684-9
Keywords: Navier-Stokes equations, rotating obstacles, strong $L^p$-solutions
Received by editor(s): July 28, 2006
Published electronically: September 26, 2008
Article copyright: © Copyright 2008 American Mathematical Society