GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION

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	GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION
	Huo Zhaohui
	2016
发表期刊	Acta Mathematica Scientia
ISSN	0252-9602
卷号	36 期号:4 页码:1117
摘要	The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space { u t t ? Δ u + u = ? n u , ? ( x , t ) ∈ ? 3 × ? + , n t t ? Δ u = Δ \| u \| 2 , ? ( x , t ) ∈ ? 3 × ? + , u ( x , 0 ) = u 0 ( x ) , ? ? t u ( x , 0 ) = u 1 ( x ) , ? n ( x , 0 ) = n 0 ( x ) , ? ? t n ( x , 0 ) = n 1 ( x ) , is considered. It is shown that it is globally well-posed in energy space H 1 × L 2 × L 2 × H ? 1 if small initial data ( u 0 ( x ) , u 1 ( x ) , n 0 ( x ) , n 1 ( x ) ) ∈ ( H 1 × L 2 × L 2 × H ? 1 ) . It answers an open problem: Is it globally well-posed in energy space H 1 × L 2 × L 2 × H ? 1 for 3D Klein-Gordon-Zakharov equation with small initial data 1,2? The method in this article combines the linear property of the equation (dispersive property) with nonlinear property of the equation (energy inequalities). We mainly extend the spaces F s and N s in one dimension 3 to higher dimension.
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23327
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Huo Zhaohui. GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION[J]. Acta Mathematica Scientia,2016,36(4):1117.
APA	Huo Zhaohui.(2016).GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION.Acta Mathematica Scientia,36(4),1117.
MLA	Huo Zhaohui."GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION".Acta Mathematica Scientia 36.4(2016):1117.