GLOBAL WELL POSEDNESS AND SCATTERING FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS BELOW THE ENERGY SPACE

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	GLOBAL WELL POSEDNESS AND SCATTERING FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS BELOW THE ENERGY SPACE
	Visan, Monica 1; Zhang, Xiaoyi 2
	2009
发表期刊	DIFFERENTIAL AND INTEGRAL EQUATIONS
ISSN	0893-4983
卷号	22 期号:1-2 页码:99-124
摘要	We prove global well posedness and scattering for the nonlinear Schrodinger equation with power-type nonlinearity {iu(t) + Delta u = vertical bar u vertical bar(p)u, 4/n < p < 4/n-2, u(0,x) = u(0)(x) is an element of H(s)(R(n)), n >= 3, below the energy space, i.e., for s < 1. In [15], J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao established polynomial growth of the H(x)(s)-norm of the solution, and hence global well posedness for initial data in H(x)(s), provided s is sufficiently close to 1. However, their bounds are insufficient to yield scattering. In this paper, we use the a priori interaction Morawetz inequality to show that scattering holds in H(s)(R(n)) whenever s is larger than some value 0 < s(0)(n,p) < 1.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000277328100006
出版者	KHAYYAM PUBL CO INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7182
专题	中国科学院数学与系统科学研究院
通讯作者	Visan, Monica
作者单位	1.Univ Calif Los Angeles, Los Angeles, CA 90095 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100864, Peoples R China
推荐引用方式 GB/T 7714	Visan, Monica,Zhang, Xiaoyi. GLOBAL WELL POSEDNESS AND SCATTERING FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS BELOW THE ENERGY SPACE[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS,2009,22(1-2):99-124.
APA	Visan, Monica,&Zhang, Xiaoyi.(2009).GLOBAL WELL POSEDNESS AND SCATTERING FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS BELOW THE ENERGY SPACE.DIFFERENTIAL AND INTEGRAL EQUATIONS,22(1-2),99-124.
MLA	Visan, Monica,et al."GLOBAL WELL POSEDNESS AND SCATTERING FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS BELOW THE ENERGY SPACE".DIFFERENTIAL AND INTEGRAL EQUATIONS 22.1-2(2009):99-124.