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REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS
Li, Dong1; Zhang, Xiaoyi2
2010
Source PublicationANALYSIS & PDE
ISSN1948-206X
Volume3Issue:2Pages:175-195
AbstractWe 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).
KeywordSchrodinger equation mass-critical
Language英语
Funding ProjectMathematics Department of the University of Iowa ; NSF[DMS-0908032] ; University of Iowa ; Alfred P. Sloan Research Fellowship ; Project 973 in China
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000281884800003
PublisherMATHEMATICAL SCIENCE PUBL
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/10561
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLi, Dong
Affiliation1.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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