Weighted $L^p$'s theory for a Stokes problem in a perturbed half-space and in an aperture domain.

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 Stokes problem with a Dirichlet boundary condition in a perturbed half-space and in an aperture domain, two unbounded geometries with noncompact boundaries. We study the existence and the uniqueness of generalized solutions in weighted $L^p$'s theory with 1 < p < 1. We study too the case of strong solutions and very weak solutions.

Mots clés: Weighted Sobolev spaces; Stokes operator; Dirichlet boundary condition; Aperture domain; Perturbed half-space

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Florian Bonzom. Weighted $L^p$'s theory for a Stokes problem in a perturbed half-space and in an aperture domain.. theory for a Stokes problem, 2009, 19 (2), pp.371--402. ⟨hal-00428956⟩