IJPAM: Volume 50, No. 2 (2009)

THE STOKES EQUATIONS IN EXTERIOR
$n$-DIMENSIONAL DOMAINS

Dagmar Medková$^1$, Werner Varnhorn$^2$
$^1$Mathematical Institute
Academy of Sciences of the Czech Republic
25, Zitná, Praha 1, 115 67, CZECH REPUBLIC
e-mail: medkova@math.cas.cz
$^2$Faculty of Mathematics
University of Kassel
Kassel, 34109, GERMANY
e-mail: varnhorn@mathematik.uni-kassel.de


Abstract.The aim of this paper is the construction and representation of solutions $u,p$ to the homogeneous Stokes equations

\begin{displaymath} -\Delta u+\nabla p\:=\:0\quad\mbox{in}\quad G_e,\quad \nabl... ...G_e, \quad u\:=\:\Phi \quad\mbox{on}\quad \Gamma ,\eqno{(S)} \end{displaymath}

with methods of hydrodynamical potential theory. Here $G_e\: \subset R^n \ (n\geq 2)$ is an exterior domain with boundary $\Gamma =\partial G_e\: \in C^2$, and $\Phi \in C^0(\Gamma )$ is some prescribed boundary value.

Received: August 14, 2008

AMS Subject Classification: 76D10, 76D07, 65N38

Key Words and Phrases: Stokes equations, boundary integrals, hydrodynamical potential theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 2