Stokes Equations and Elliptic Systems With Non Standard Boundary Conditions

Chérif Amrouche (1) , Nour El Houda Seloula (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods

In a three dimensional bounded possibly multiply-connected domain of class C 1,1 , we consider the stationary Stokes equations with nonstandard boundary conditions of the form u * n = g and curl u × n = h × n or u × n = g × n and π = π0 on the boundary Γ. We prove the existence and uniqueness of weak, strong and very weak solutions corresponding to each boundary condition in Lp theory. Our proofs are based on obtaining Inf −Sup conditions that play a fundamental role. And finally, we give two Helmholtz decompositions that consist of two kinds of boundary conditions such as u * n and u × n on Γ.

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Nour El Houda Seloula. Stokes Equations and Elliptic Systems With Non Standard Boundary Conditions. Comptes Rendus. Mathématique, 2011, 349 (11-12), pp.703-708. ⟨hal-00629131⟩