Acta mathematica scientia, Series B >
GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE
Received date: 2009-09-30
Online published: 2011-07-20
Supported by
The authors were supported by NSFC (10771074) and NSFC-NSAF (10976026). Yang was partially supported by NSFC (10801055; 10901057).
The periodic initial value problem of a fifth-order shallow water equation
∂tu − ∂2x∂tu+ ∂3xu −∂5xu +3u∂xu −∂2xu ∂2xu -u∂3xu= 0
is shown to be globally well-posed in Sobolev spaces Hs(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.
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 . DOI: 10.1016/S0252-9602(11)60317-2
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