Journal article
REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS
Analysis & PDE, Vol.3(2), pp.175-195
01/01/2010
DOI: 10.2140/apde.2010.3.175
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).
Details
- Title: Subtitle
- REGULARITY OF ALMOST PERIODIC MODULO SCALING SOLUTIONS FOR MASS-CRITICAL NLS AND APPLICATIONS
- Creators
- Dong Li - University of IowaXiaoyi Zhang - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Analysis & PDE, Vol.3(2), pp.175-195
- Publisher
- MATHEMATICAL SCIENCE PUBL
- DOI
- 10.2140/apde.2010.3.175
- ISSN
- 1948-206X
- eISSN
- 1948-206X
- Number of pages
- 21
- Grant note
- University of Iowa Project 973 in China Mathematics Department of the University of Iowa DMS-0908032 / NSF Alfred P. Sloan Research Fellowship
- Language
- English
- Date published
- 01/01/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9984241043402771
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