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

TL;DR

This paper proves global existence and stability of solutions for the Schrödinger-Debye system with initial data of infinite mass, including singular and blow-up data, using weak-Lp space analysis.

Contribution

It introduces new global existence results for infinite mass initial data, extending previous work to include singular and blow-up functions.

Findings

Global solutions exist for data with infinite mass.

Includes data with singularities and finite point blow-ups.

Analyzes asymptotic stability of solutions.

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.