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

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 Title: Maximal regularity for the Stokes system on noncylindrical space-time domains Authors: Saal, Juergen Browse this author Issue Date: 2004 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 668 Start Page: 1 End Page: 23 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69473 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics