The $L^p$-Helmholtz projection in finite cylinders

Title:

The $L^p$-Helmholtz projection in finite cylinders

Creator:

Nau, Tobias

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c40a2bba-e2c9-410f-8571-f21d48de3741
uuid:c40a2bba-e2c9-410f-8571-f21d48de3741

Subject:

Helmholtz projection, Helmholtz decomposition, weak Neumann problem, periodic boundary conditions, finite cylinder, cylindrical space domain, $L^p$-space, operator-valued Fourier multiplier, $\mathcal R$-boundedness, reflection technique, and fluid dynamics

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this article we prove for $1<p<\infty $ the existence of the $L^p$-Helmholtz projection in finite cylinders $\Omega $. More precisely, $\Omega $ is considered to be given as the Cartesian product of a cube and a bounded domain $V$ having $C^1$-boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in $\Omega $ is solved, which implies existence and a representation of the $L^p$-Helmholtz projection as a Fourier multiplier operator.

Language:

English

Rights:

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

Coverage:

119-134

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:1

Harvested from:

CDK

Metadata only:

false