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

Title:

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

Creator:

Sauer, Jonas

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7fc9f78c-035f-4c39-9847-1132bd5f96b1
uuid:7fc9f78c-035f-4c39-9847-1132bd5f96b1
issn:0011-4642

Subject:

matematika, mathematics, Stokesova věta, Stokes operator, spatially periodic problem, maximal Lp regularity, nematic liquid crystal flow, quasilinear parabolic equations, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

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., Jonas Sauer., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

41-55

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:1

Harvested from:

CDK

Metadata only:

false