open access

https://doi.org/10.14943/83819

https://hdl.handle.net/2115/69473

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

英語

2004

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

668

1-23

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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