Low regularity solutions to the logarithmic Schrodinger equation

Abstract

We consider the logarithmic Schr{ö}dinger equation, in various geometric settings. We show that the flow map can be uniquely extended from H^1 to L^2 , and that this extension is Lipschitz continuous. Moreover, we prove the regularity of the flow map in intermediate Sobolev spaces.

Some typos fixed. A flaw corrected in Section 4