Growing Sobolev norms for the cubic defocusing Schrödinger equation. (English) Zbl 1490.35421
Summary: This text aims to describe results of the authors on the long time behavior of NLS on product spaces with a particular emphasis on the existence of solutions with growing higher Sobolev norms.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35P25 | Scattering theory for PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
Keywords:
Schrödinger equationReferences:
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