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

作　　者：Ping ZHANG~1 Zhi-fei ZHANG~2 1 Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China 2 School of Mathematical Sciences,Peking University,Beijing 100871,China 

出　　处：《Science China Mathematics》2007年第8期1065-1077,共13页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.10525101,10421101 and 10601002);the innovation grant from Chinese Academy of Sciences

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≤-2c₀&lt;0 withξbeing restricted to the initial surface.

关 键 词：WATER-WAVES free boundary incompressible Euler equations primary 35Q35 76B03 secondary 35J67 35L80 

分 类 号：O175.29[理学—数学]