On the Regularity of the Solutions for Cauchy Problem of Incompressible 3D Navier-Stokes Equation
In this paper we will prove that the vorticity belongs to L1(0; T ; L2(R3)) for the Cauchy problem of 3D incompressible Navier-Stokes equation, then the existence of a global smooth solution is obtained. Our approach is to construct a set of auxiliary problems to approximate the original one of vorticity equation.