Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space

摘要

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