ON THE EQUATION□Φ=|▽Φ|~2 IN FOUR SPACE DIMENSIONS

作     者：ZHOU YI Institute of Mathematics, Fudan University, Shanghai 200433, China. 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2003年第24卷第3期

页      面：293-302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：Project supported by the 973 Project of the National Natural Science Foundation of China the Key Teachers Program and the Doctoral Program Foundation ofthe Miistry of Education of China 

主　　题：Semilinear wave equation Cauchy problem Low regularity solution 

摘      要：This paper considers the following Cauchy problem for semilinear wave equations in n space dimensionswhere A is the wave operator, F is quadratic in (?) with (?) = ( ).The minimal value of s is determined such that the above Cauchy problem is locally well-posed in H8. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n≥5). The purpose of this paper is to supplement with a proof in the case n = 2,4.