ON THE STOKES PROBLEM IN EXTERIOR DOMAINS: THE MAXIMUM MODULUS THEOREM

We study the Stokes IBVP,in (0;T)XD,where D enclosed in Rn,n>2,is an exterior domain,assuming that the initial data is in L^\infty, free divergent in w.s.We prove the maximum modulus theorem for the corresponding solutions. The proof is based on an analogous one proved by Abe-Giga for bounded domains and by duality arguments and employing the semigroup properties of the resolving operator defined on L^1(D).Our results are similar to the ones proved by Solonnikov by means of the potential theory