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

• Saal Jürgen

  Department of Mathematics, Darmstadt University of Technology

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.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 58 (3), 617-641, 2006

  The Mathematical Society of Japan

Keywords

• Stokes equations
• moving boundary
• nonautonomous systems
• evolution operators
• maximal regularity

Details

• CRID: 1390001205116488064
• NII Article ID: 10018380990
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/1156342030
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2254403
• NDL BIB ID: 7987041
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7987041
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed