On a generalized Stokes system with slip boundary conditions in the half-space

Abstract

We are interested in a system of Stokes type, where the divergence-free constraint is modified by adding a term proportional to the pressure. The domain is the half-space with nonhomogeneous Navier's boundary conditions. The weighted Sobolev spaces yield a natural functional framework to envisage a wide class of behavior at infinity for data and solutions. So, we can give a range of solutions from strong to very weak depending on the regularity of the data. All along this study, we take the bridge between this system and the linear elasticity system.