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

Creator:
Nau, Tobias
Format:
bez média and svazek
Type:
model:article and TEXT
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
Language:
English
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public