The existence for the classical solution of the Navier-Stokes equations

In this paper we will discuss the existence for the classical solution of the Navier-Stokes equations. First, we transform it into generalized integral equations. Next, we discuss the existence of the classical solution by Leray-Schauder degree and Sobolev space\ $H^{-m_1}({\mathrm{\Omega }}_1)$.