Local Cauchy theory for the nonlinear Schrödinger equation in spaces of infinite mass

Abstract

We consider the Cauchy problem for the nonlinear Schrödinger equation on ${\mathbb{R}}^d$, where the initial data is in ${\dot{H}}^1({\mathbb{R}}^d)\cap L^p({\mathbb{R}}^d)$. We prove local well-posedness for large ranges of $p$ and discuss some global well-posedness results.

arXiv comment13 pages