Journal article
GLOBAL WELL POSEDNESS AND SCATTERING FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS BELOW THE ENERGY SPACE
Differential and integral equations, Vol.22(1-2), pp.99-124
01/01/2009
Abstract
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.
Details
- Title: Subtitle
- GLOBAL WELL POSEDNESS AND SCATTERING FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS BELOW THE ENERGY SPACE
- Creators
- Monica Visan - Univ Calif Los Angeles, Los Angeles, CA 90095 USAXiaoyi Zhang - Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100864, Peoples R China
- Resource Type
- Journal article
- Publication Details
- Differential and integral equations, Vol.22(1-2), pp.99-124
- Publisher
- KHAYYAM PUBL CO INC
- ISSN
- 0893-4983
- Number of pages
- 26
- Language
- English
- Date published
- 01/01/2009
- Academic Unit
- Mathematics
- Record Identifier
- 9984241054902771
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