Nonlinear Schrodinger equation with time dependent potential

Details Nonlinear Schrodinger equation with time dependent potential Nonlinear Schrodinger equation with time dependent potential

2009-10-26

arxiv.org/abs/0910.4893v2

Communications in Mathematical Sciences 9, 4 (2011) 937-964

Mathematics

Analysis of PDEs

27 pages. Some typos fixed

Scientific paper

We prove a global well-posedness result for defocusing nonlinear Schrodinger equations with time dependent potential. We then focus on time dependent harmonic potentials. This aspect is motivated by Physics (Bose--Einstein condensation), and appears also as a preparation for the analysis of the propagation of wave packets in a nonlinear context. The main aspect considered here is the growth of high Sobolev norms of the solution.

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