Global attractors for the Klein-Gordon-Schrödinger equation in unbounded domains

Abstract

In this paper, we study the long time behavior of solutions for the Klein-Gordon-Schrödinger equation in the whole space Rn with n≤3. We first prove the continuity of the solutions on initial data and then establish the asymptotic compactness of solutions. Finally, we show the existence of the global attractor for this model in the space Hk(Rn)×Hk(Rn) for each integer k≥1. © 2001 Academic Press.