ON THE STOKES EQUATIONS WITH THE NAVIER-TYPE BOUNDARY CONDITIONS

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 center dot n = g and curlu x n = h x n on the boundary Gamma. We prove the existence and uniqueness of weak, strong and very weak solutions. Our proofs are mainly based on In f -Sup conditions.