Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 34, Issue 12, Pages 1531-1565Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605300903328109
Keywords
Energy critical; Nonlinear Schrodinger equation
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Funding
- National Science Foundation
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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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