Global existence for Schrödinger–Debye system for initial data with infinite 𝐿²-norm

Abstract

In this paper we study global-in-time existence for the Cauchy problem associated to the Schrödinger–Debye system for a class of initial data with infinite L 2 L^{2} -norm, namely weak- L p L^{p} spaces. This model appears in nonlinear optics as a perturbation of the classical nonlinear Schrödinger equation (NLS). Our results exhibit differences between both models in that setting, e.g. the Debye perturbation imposes restrictions in the spatial dimension. We also analyze the asymptotic stability of the solutions.