On the Stokes system in cylindrical domains

Abstract

The existence of solutions to some initial-boundary value problem for the Stokes system is proved. The result is shown in Sobolev-Slobodetskii spaces such that the velocity belongs to $W_r^{2+\sigma ,1+\sigma /2}({\Omega }^T)$ and gradient of pressure to $W_r^{\sigma ,\sigma /2}({\Omega }^T)$, where $r\in (1,\infty )$, $\sigma \in (0,1)$, ${\Omega }^T=\Omega \times (0,T)$. These are special Besov spaces: $B_{r,r}^{2+\sigma ,1+\sigma /2}({\Omega }^T)$ and $B_{r,r}^{\sigma ,\sigma /2}({\Omega }^T)$, respectively. The existence is proved by the technique of regularizer.

70 pages