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Abstract

Existence of solutions for equations of the nonstationary Stokes system in a bounded domain $ \Omega \subset {{\Bbb R}}^3$ is proved in a class such that velocity belongs to $W_p^{2,1}({ \Omega }\times (0,T))$, and pressure belongs to $W_p^{1,0}({ \Omega }\times (0,T))$ for $p>3$. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered.