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On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data
Li, Dong1; Zhang, Xiaoyi1,2
2010-12-01
Source PublicationDYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
ISSN1548-159X
Volume7Issue:4Pages:345-373
AbstractIn this paper, we consider the six-dimensional focusing mass critical NLS: iu(t) + Delta u = -vertical bar u vertical bar(2/3) u with splitting-spherical initial data u(0)(x(1), ... x(6)) = u(0)(root x(1)(2) + x(2)(2) + x(3)(2), root x(4)(2) + x(5)(2) + x(6)(2)). we prove that any finite mass solution which is almost periodic modulo scaling in both time directions must have Sobolev regularity H(x)(1+). Moreover, the kinetic energy of the solution is localized around the spatial origin uniformly in time. As important applications of the results, we prove the scattering conjecture for solutions with mass smaller than that of the ground state. We also prove that any two-way non-scattering solution must be global and coincides with the solitary wave up to symmetries. Here the ground state is the unique positive, radial solution of the nonlinear elliptic equation Delta Q - Q + Q(5/3) = 0. To prove the smoothness of the solution, we use a new local iteration scheme which first appears in [19].
KeywordFocusing mass critical NLS Sobolev regularity scattering conjecture
Language英语
Funding ProjectMathematics Department of University of Iowa ; NSF[090832] ; Alfred P. Sloan Research Fellowship
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000287554600004
PublisherINT PRESS BOSTON, INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/9509
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 52246 USA
2.Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Li, Dong,Zhang, Xiaoyi. On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data[J]. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS,2010,7(4):345-373.
APA Li, Dong,&Zhang, Xiaoyi.(2010).On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data.DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS,7(4),345-373.
MLA Li, Dong,et al."On the focusing mass critical problem in six dimensions with splitting spherically symmetric initial data".DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS 7.4(2010):345-373.
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