On the Stokes equations with the Navier-type boundary conditions
Chérif Amrouche, Nour El Houda Seloula · Differential Equations & Applications · 2011
In a possibly multiply-connected three dimensional bounded domain, we prove in the L p theory the existence and uniqueness of vector potentials, associated with a divergence-free function and satisfying non homogeneous boundary conditions. Furthermore, we consider the stationary Stokes equations with nonstandard boundary conditions of the form u n = g and curl u n = h n on the boundary . We prove the existence and uniqueness of weak, strong and very weak solutions. Our proofs are mainly based on In f -Sup conditions.