On the local wellposedness of 3-D water wave problem with vorticity

In this article, we first present an equivalent formulation of the free boundary problem to 3-D incompressible Euler equations, then we announce our local wellposedness result concerning the free boundary problem in Sobolev space provided that there is no self-intersection point on the initial surface and under the stability assumption that being restricted to the initial surface. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10525101, 10421101 and 10601002) and the innovation grant from Chinese Academy of Sciences