Carles, Rémi Nonlinear Schrödinger equation with time dependent potential. (English) Zbl 1285.35105 Commun. Math. Sci. 9, No. 4, 937-964 (2011). 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. Reviewer: Qin Meng Zhao (Beijing) Cited in 53 Documents 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 Keywords:nonlinear Schrödinger equation; time dependent external potential; Avron-Herbst formula; lens transform; large time behavior; Bose-Einstein condensation; nonlinear propagation of wave packets PDFBibTeX XMLCite \textit{R. Carles}, Commun. Math. Sci. 9, No. 4, 937--964 (2011; Zbl 1285.35105) Full Text: DOI arXiv Link