Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential

Preprint

1 October 2014

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.1409.5759

Abstract

We review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. The characterization of the minimal decay is different in the case of super-quadratic potentials.

Keywords

SCHRODINGER EQUATIONS
NONLINEAR SCHRODINGER
QUADRATIC POTENTIALS
CAUCHY PROBLEM
SHARP WEIGHTS
DECAY

All Related Versions

Version 1, 2014-09-19, ArXiv
Version 2, 2014-09-23, ArXiv
Version 3, 2014-10-01, ArXiv
Version 1, 2006-09-14, ArXiv (Unconfirmed version)
Version 2, 2007-01-23, ArXiv (Unconfirmed version)
Published version: Zeitschrift für angewandte Mathematik und Physik, 66 (4), 2087.

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