Global Solutions for Schrödinger-Debye System for Data with an Infinite $l^2$- norm

Details Global Solutions for Schrödinger-Debye System for Data with an Infinite $l^2$- norm Global Solutions for Schrödinger-Debye System for Data with an Infinite $l^2$- norm

2010-09-07

arxiv.org/abs/1009.1323v1

Mathematics

Analysis of PDEs

Scientific paper

We obtain global well-posedness results for the Cauchy problem associated to the the Schr\"odinger-Debye system for two class of data with infinite $L^2$-norm. Our results include data such as small perturbations of positive constants, 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 Zhidkov and weak-$L^p$ spaces.

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