Nonstationary Stokes system in anisotropic Sobolev spaces

摘要

The nonstationary Stokes system with slip boundary conditions is considered in a bounded domain Omega subset of R-3. We prove the existence and uniqueness of solutions to the problem in anisotropic Sobolev spaces W-r(2,1) (Omega x (0, T)), r is an element of(1, infinity). Thanks to the slip boundary conditions, the Stokes problem is transformed to the Poisson and the heat equation. In this way, difficult calculations that must be performed in considerations of boundary value problems for the Stokes system are avoided. This approach does not work for the Dirichlet and the Neumann boundary conditions. Because solvability of the Poisson and the heat equation is carried out by the regularizer technique, we have that S = partial derivative Omega is an element of C1+alpha boolean AND W-r(3-1/r) boolean AND W-sigma(2-1/sigma), sigma > 3, alpha > 0. Copyright (C) 2014 JohnWiley & Sons, Ltd.