  We are concerned with the non-stationary Stokes system with non-homogeneous
external force and non-zero initial data in ${\mathbb R}^n_+ \times (0,T)$. We
obtain new estimates of solutions including pressure in terms of mixed
anisotropic Sobolev spaces. As an application, some anisotropic Sobolev
estimates are presented for weak solutions of the Navier-Stokes equations in a
half-space in dimension three.
