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

• Saal Jürgen

  Department of Mathematics, Darmstadt University of Technology

抄録

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.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

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

  一般社団法人 日本数学会

キーワード

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

詳細情報

• CRID: 1390001205116488064
• NII論文ID: 10018380990
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/1156342030
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2254403
• NDL書誌ID: 7987041
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7987041
• 本文言語コード: en
• データソース種別:
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