STOKES AND NAVIER-STOKES PROBLEMS WITH NAVIER-TYPE BOUNDARY CONDITION IN LP-SPACES

Using the semigroup theory for the Stokes equation with Navier type boundary conditions developed in [2, 3], we first prove the maximal L-p - L-q regularity for the strong, weak and very weak solutions of the inhomogeneous Stokes problem with Navier-type boundary conditions in a bounded domain Omega, not necessarily simply connected. We also prove the existence of a unique local in time classical solution to the Navier Stokes problem with Navier-type boundary conditions and show that it is global in time for small initial data.