On the hydrostatic Stokes approximation with non homogeneous Dirichlet boundary conditions

Chérif Amrouche (1) , Fabien Dahoumane (1) , Robert Luce (1) , Guy Vallet (1)

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

We deal with the hydrostatic Stokes approximation with non homogeneous Dirichlet boundary conditions. After having investigated the homogeneous case, we build a shifting operator of boundary values related to the divergence operator, and solve the non homogeneous problem in a cylindrical type domain.

Mots clés: Hydrostatic approximation; De Rham's lemma; shifting operator; Primitive Equations; non homogeneous Dirichlet conditions

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Fabien Dahoumane, Robert Luce, Guy Vallet. On the hydrostatic Stokes approximation with non homogeneous Dirichlet boundary conditions. 2009. ⟨hal-00428960⟩