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

	GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION
	Huo, Zhaohui
刊名	ACTA MATHEMATICA SCIENTIA
	2016-07-01
卷号	36 期号:4 页码:1117-1152
关键词	Global well-posedness 3D Klein-Gordon-Zakharov equation dyadic X-s,X-b spaces in higher dimension
ISSN号	0252-9602
英文摘要	The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space {u(tt) - Delta u + u = -nu, (x, t) is an element of R-3 x R+, n(tt) - Delta n = Delta vertical bar u vertical bar(2), (x,t) is an element of R-3 x R+, (0.1) u(x, 0) = u(0)(x), partial derivative(t)u(x, 0) = u(1)(x), n(x, 0) = n(0)(x), partial derivative(t)n(x, 0) = n(1)(x), is considered. It is shown that it is globally well-posed in energy space H-1 x L-2 x L-2 x H-1 if small initial data (u(0)(x), u(1)(x), n(0)(x), n(1)(x)) is an element of (H-1 x L-2 x (L)2 x H-1). It answers an open problem: Is it globally well-posed in energy space H-1 x L-2 x L-2 x 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
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000381529900007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/23326]
专题	中国科学院数学与系统科学研究院
通讯作者	Huo, Zhaohui
作者单位	Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
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):1117-1152.
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),1117-1152.
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):1117-1152.