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July, 2006 Maximal regularity for the Stokes system on noncylindrical space-time domains
Jürgen SAAL
J. Math. Soc. Japan 58(3): 617-641 (July, 2006). DOI: 10.2969/jmsj/1156342030


We prove L p - L q maximal regularity estimates for the Stokes equations in spatial regions with moving boundary. Our result includes bounded and unbounded regions. The method relies on a reduction of the problem to an equivalent nonautonomous system on a cylindrical space-time domain. By applying suitable abstract results for nonautonomous Cauchy problems we show maximal regularity of the associated propagator which yields the result. The abstract results, also proved in this note, are a modified version of a nonautonomous maximal regularity result of Y. Giga, M. Giga, and H. Sohr and a suitable perturbation result. Finally we describe briefly the application to the special case of rotating regions.


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Jürgen SAAL. "Maximal regularity for the Stokes system on noncylindrical space-time domains." J. Math. Soc. Japan 58 (3) 617 - 641, July, 2006.


Published: July, 2006
First available in Project Euclid: 23 August 2006

zbMATH: 1184.35247
MathSciNet: MR2254403
Digital Object Identifier: 10.2969/jmsj/1156342030

Primary: 35Q30 , 76D05 , 76D07
Secondary: 47D06

Keywords: evolution operators , maximal regularity , Moving boundary , nonautonomous systems , Stokes equations

Rights: Copyright © 2006 Mathematical Society of Japan


Vol.58 • No. 3 • July, 2006
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