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

doi:10.1016/S0252-9602(11)60317-2

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1303-1317.doi: 10.1016/S0252-9602(11)60317-2

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

李用声, 杨兴雨

Department of Mathematics, South China University of Technology, Guangzhou 510640, China

收稿日期:2009-09-30 出版日期:2011-07-20 发布日期:2011-07-20
通讯作者: 杨兴雨 E-mail:yshli@scut.edu.cn; xyyangmath@gmail.com
基金资助:
The authors were supported by NSFC (10771074) and NSFC-NSAF (10976026). Yang was partially supported by NSFC (10801055; 10901057).

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

LI Yong-Sheng, YANG Xin-Yu

Department of Mathematics, South China University of Technology, Guangzhou 510640, China

Received:2009-09-30 Online:2011-07-20 Published:2011-07-20
Contact: Yang Xingyu E-mail:yshli@scut.edu.cn; xyyangmath@gmail.com
Supported by:
The authors were supported by NSFC (10771074) and NSFC-NSAF (10976026). Yang was partially supported by NSFC (10801055; 10901057).

摘要/Abstract

摘要：

The periodic initial value problem of a fifth-order shallow water equation
∂^tu − ∂²_x∂_tu+ ∂³_xu −∂⁵_xu +3u∂_xu −∂2_xu ∂²_xu -u∂³_xu= 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

Abstract:

The periodic initial value problem of a fifth-order shallow water equation
∂^tu − ∂²_x∂_tu+ ∂³_xu −∂⁵_xu +3u∂_xu −∂2_xu ∂²_xu -u∂³_xu= 0

Key words: shallow water equation, periodic initial value problem, global well-posedness, I-method, almost conservation law

中图分类号:

35Q53

李用声, 杨兴雨. GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE[J]. 数学物理学报(英文版), 2011, 31(4): 1303-1317.

LI Yong-Sheng, YANG Xin-Yu. GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE[J]. Acta mathematica scientia,Series B, 2011, 31(4): 1303-1317.

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

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

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