Global existence for Schrodinger-Debye system for initial data with infinite mass

Abstract

We obtain global existence results for the Cauchy problem associated to the Schrodinger-Debye system for a class of data with infinite mass (L2-norm). A smallness condition on data is assumed. Our results include data such as singular-homogeneous functions and some types of data blowing up at finitely many points. We also study the asymptotic stability of the solutions. Our analysis is performed in the framework of weak-Lp spaces.