KMS Of Academy of mathematics and systems sciences, CAS
REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS | |
Li, Dong1; Zhang, Xiaoyi2 | |
2010 | |
Source Publication | ANALYSIS & PDE |
ISSN | 1948-206X |
Volume | 3Issue:2Pages:175-195 |
Abstract | We consider the L(x)(2) solution u to mass-critical NLS iu(t) + Delta u = +/-vertical bar u vertical bar(4/d)u. We prove that in dimensions d >= 4, if the solution is spherically symmetric and is almost periodic modulo scaling, then it must lie in H(x)(1 + epsilon) for some epsilon > 0. Moreover, the kinetic energy of the solution is localized uniformly in time. One important application of the theorem is a simplified proof of the scattering conjecture for mass-critical NLS without reducing to three enemies. As another important application, we establish a Liouville type result for L(x)(2) initial data with ground state mass. We prove that if a radial L(x)(2) solution to focusing mass-critical problem has the ground state mass and does not scatter in both time directions, then it must be global and coincide with the solitary wave up to symmetries. Here the ground state is the unique, positive, radial solution to elliptic equation Delta Q - Q + Q(1+4/d) = 0. This is the first rigidity type result in scale invariant space L(x)(2). |
Keyword | Schrodinger equation mass-critical |
Language | 英语 |
Funding Project | Mathematics Department of the University of Iowa ; NSF[DMS-0908032] ; University of Iowa ; Alfred P. Sloan Research Fellowship ; Project 973 in China |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000281884800003 |
Publisher | MATHEMATICAL SCIENCE PUBL |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/10561 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Li, Dong |
Affiliation | 1.Univ Iowa, Dept Math, Iowa City, IA 52240 USA 2.Acad Math & Syst Sci, Beijing, Peoples R China |
Recommended Citation GB/T 7714 | Li, Dong,Zhang, Xiaoyi. REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS[J]. ANALYSIS & PDE,2010,3(2):175-195. |
APA | Li, Dong,&Zhang, Xiaoyi.(2010).REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS.ANALYSIS & PDE,3(2),175-195. |
MLA | Li, Dong,et al."REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS".ANALYSIS & PDE 3.2(2010):175-195. |
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