  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}.
