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Nonlinear Schrödinger equation with time dependent potential. (English) Zbl 1285.35105

The authors prove a global well-posedness result for defocusing nonlinear Schrödinger equations with time dependent potential. They 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. Such a control is needed to study the large time propagation of nonlinear coherent states.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B40 Asymptotic behavior of solutions to PDEs
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