期刊
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
卷 34, 期 12, 页码 1531-1565出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/03605300903328109
关键词
Energy critical; Nonlinear Schrodinger equation
资金
- National Science Foundation
We consider the defocusing [image omitted]-critical nonlinear Schrodinger equation in all dimensions (n epsilon 3) with a quadratic potential [image omitted]. We show global well-posedness for radial initial data obeying delta u0(x), xu0(x)L2. In view of the potential V, this is the natural energy space. In the repulsive case, we also prove scattering. We follow the approach pioneered by Bourgain and Tao in the case of no potential; indeed, we include a proof of their results that incorporates a couple of simplifications discovered while treating the problem with quadratic potential.
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