GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE  

作　　者：李用声 杨兴雨 

机构地区：[1]Department of Mathematics, South China University of Technology

出　　处：《Acta Mathematica Scientia》2011年第4期1303-1317,共15页数学物理学报（B辑英文版）

基　　金：supported by NSFC (10771074);NSFC-NSAF(10976026);Yang was partially supported by NSFC (10801055; 10901057)

摘　　要：The periodic initial value problem of a fifth-order shallow water equation t u 2 x t u ＋ 3 x u 5 x u ＋ 3u x u 2 x u 2 x u u 3 x u = 0 is shown to be globally well-posed in Sobolev spaces˙ H s （T） for s 〉 2/3 by I-method. For this equation lacks scaling invariance, we first reconsider the local result and pay special attention to the relationship between the lifespan of the local solution and the initial data, and then prove the almost conservation law, and finally obtain the global well-posedness by an iteration process.The periodic initial value problem of a fifth-order shallow water equation t u 2 x t u ＋ 3 x u 5 x u ＋ 3u x u 2 x u 2 x u u 3 x u = 0 is shown to be globally well-posed in Sobolev spaces˙ H s （T） for s 〉 2/3 by I-method. For this equation lacks scaling invariance, we first reconsider the local result and pay special attention to the relationship between the lifespan of the local solution and the initial data, and then prove the almost conservation law, and finally obtain the global well-posedness by an iteration process.

关 键 词：shallow water equation periodic initial value problem global well-posedness I-METHOD almost conservation law 

分 类 号：O175.8[理学—数学]