Maximal regularity of the time-periodic Stokes operator on unbounded and bounded domains
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- Maekawa Yasunori
- Mathematical Institute, Tohoku University
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- Sauer Jonas
- Fachbereich Mathematik, Technische Universität Darmstadt
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<p>We investigate the time-periodic Stokes equations with non-homogeneous divergence data in the whole space, the half space, bent half spaces and bounded domains. The solutions decompose into a well-studied stationary part and a purely periodic part, for which we establish Lp estimates. For the whole space and the half space case we use a reduction of the Stokes equations to (n − 1) heat equations. Perturbation and localisation methods yield the result on bent half spaces and bounded domains. A one-to-one correspondence between maximal regularity for the initial value problem and time periodic maximal regularity is proven, providing a short proof for the maximal regularity of the Stokes operator avoiding the notion of ℛ-boundedness. The results are applied to a quasilinear model governing the flow of nematic liquid crystals.</p>
収録刊行物
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 69 (4), 1403-1429, 2017
一般社団法人 日本数学会
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詳細情報 詳細情報について
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- CRID
- 1390282680091628416
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- NII論文ID
- 130006887118
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- NII書誌ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL書誌ID
- 028590301
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
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- KAKEN
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- 使用不可