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 

作者机构：Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China School of Mathematical Sciences Peking University Beijing China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2007年第50卷第8期

页      面：1065-1077页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：water-waves free boundary incompressible Euler equations primary 35Q35 76B03 secondary 35J67 35L80 

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.