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Maximal regularity for the Stokes system on noncylindrical space-time domains

Preprint Series # 668
Saal, Juergen Maximal regularity for the Stokes system on noncylindrical space-time domains. (2004);

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Abstract

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.

Item Type:Preprint
Uncontrolled Keywords:maximal regularity, moving boundary, nonautonomous equations
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:441

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  • Maximal regularity for the Stokes system on noncylindrical space-time domains. (deposited 23 Sep 2004) [Currently Displayed]