Global well-posedness for the 3D Navier-Sokes equations with a large component of vorticity

In this paper, we give a new approach to improve the Leray's result concerning the cauchy problem to the 3D Navier-Stokes equations. In particular, global well-posedness with a large component of the initial vorticity is obtained. Our idea is considering the vorticity equations and using some suitable function spaces.