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

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.

8 pages, Corollary 3.5 is now a bit more general

References in corpus (1)

• Remark on the Kato smoothing effect for Schrödinger equation with superquadratic potentials

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