Maximal regularity of the spatially periodic Stokes operator and application to nematic liquid crystal flows

Czechoslovak Mathematical Journal

Jonas ¹ 

[1] Fachbereich Mathematik, Technische Universitt Darmstadt, Schlogartenstrae 7, 64283 Darmstadt, Germany

关键词: Stokes operator;    spatially periodic problem;    maximal $L^p$ regularity;    nematic liquid crystal flow;    quasilinear parabolic equations;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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-in-time 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 $\mathcal{R}$-bound for the resolvent estimate. Then, Weis' theorem connecting $\mathcal{R}$-boundedness of the resolvent with maximal $L^p$ regularity of a sectorial operator applies.

【 授权许可】

Unknown