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

Autor:	Jonas Sauer
Rok vydání:	2016
Předmět:	Laplace transform General Mathematics 010102 general mathematics Mathematical analysis Existence theorem 01 natural sciences 010101 applied mathematics Operator (computer programming) Locally compact space Uniqueness 0101 mathematics Abelian group Stokes operator Mathematics Resolvent
Zdroj:	Czechoslovak Mathematical Journal. 66:41-55
ISSN:	1572-9141 0011-4642
DOI:	10.1007/s10587-016-0237-2
Popis:	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 Lp-regularity of the periodic Laplace and Stokes operators and a local-intime existence theorem for quasilinear parabolic equations a la Clement-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 Lp regularity of a sectorial operator applies.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::eac9ab9571744be76b672fa3f11c9c22 https://doi.org/10.1007/s10587-016-0237-2 Zobrazit plný text záznamu Full text from SpringerLink