Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data

Abstract

We consider the Cauchy problem for the defocusing nonlinear Schrödinger equations (NLS) on the real line with a special subclass of almost periodic functions as initial data. In particular, we prove global existence of solutions to NLS with limit periodic functions as initial data under some regularity assumption.

22 pages, to appear in a special issue of Commun. Pure Appl. Anal