Exterior Stokes problem in the half-space

Chérif Amrouche (1) , Florian Bonzom (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

The purpose of this work is to solve the exterior Stokes problem in the half-space $\R{^n_+}$. We study the existence and the uniqueness of generalized solutions in weighted $L^p$ theory with $1 < p < \infty$. Moreover, we consider the case of strong solutions and very weak solutions. This paper extends the studies done in \cite{AA2} for an exterior Stokes problem in the whole space and in \cite{AB2} for the study of the Laplace equation in the same geometry as here.

Mots clés: Weighted Sobolev spaces; Stokes operator; Dirichlet boundary conditions; Exterior problem; Half-space

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Florian Bonzom. Exterior Stokes problem in the half-space. Annali dell'Universita di Ferrara, 2009, 55 (1), pp.37-66. ⟨10.1007/s11565-009-0064-6⟩. ⟨hal-00335168⟩