Maximal regularity of the spatially periodic stokes operator and application to nematic liquid crystal flows
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- 作者：Jonas Sauer
- 关键词：Stokes operator ; spatially periodic problem ; maximal L p regularity ; nematic liquid crystal flow ; quasilinear parabolic equations
- 刊名：Czechoslovak Mathematical Journal
- 出版年：2016
- 出版时间：March 2016
- 年：2016
- 卷：66
- 期：1
- 页码：41-55
- 全文大小：185 KB
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1. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstraße 7, 64283, Darmstadt, Germany - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Analysis
Convex and Discrete Geometry
Ordinary Differential Equations
Mathematical Modeling and IndustrialMathematics - 出版者：Springer Netherlands
- ISSN：1572-9141
文摘
We consider the dynamics of spatially periodic nematic liquid crystal flows in the whole space and prove existence and uniqueness of local-in-time strong solutions using maximal L p -regularity of the periodic Laplace and Stokes operators and a local-intime existence theorem for quasilinear parabolic equations à la Clément-Li (1993). Maximal regularity of the Laplace and the Stokes operator is obtained using an extrapolation theorem on the locally compact abelian group \(G: = \mathbb{R}^{n - 1} \times \mathbb{R}/L\mathbb{Z}\) to obtain an R-bound for the resolvent estimate. Then, Weis’ theorem connecting R-boundedness of the resolvent with maximal L p regularity of a sectorial operator applies.