On estimates of solutions of the non-stationary Stokes problem in anisotropic Sobolev spaces and on estimates for the resolvent of the Stokes operator

In this paper, which is mainly of a survey nature, a coercive estimate is proved in Sobolev spaces with a mixed norm to solve the non-stationary Stokes problem (with non-zero divergence) in bounded and exterior domains, and from the first estimate an estimate is proved for the resolvent of the Stokes operator. The latter proof uses the explicit representation of the solution of the problem in a half-space in terms of the Green's matrix; pointwise estimates are derived for the elements of this matrix.