摘要
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 $\frac{{\partial p}}{{\partial n}}(\xi )\left| {_{t = 0} } \right. \leqslant - 2c_0 < 0$ being restricted to the initial surface.
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（?）p/（?）n（ξ）|t=0≤-2c<sub>0</sub><0 withξbeing restricted to the initial surface.
基金
the National Natural Science Foundation of China(Grant Nos.10525101,10421101 and 10601002)
the innovation grant from Chinese Academy of Sciences
