Boundary value problem of a non-stationary Stokes system in a bounded smooth cylinder

In this paper, we intend to study the boundary value problem of the non-stationary Stokes system in a bounded smooth cylinder $\Omega\times (0,T)$. As a first step, we consider the problem in half-plane cylinder ${\mathbb R}^n_+ \times (0,T), \,\, 0 < T \leq \infty$. We extend the result of Solonnikov\cite{So} to data in weaker function spaces than the one considered in \cite{So}.