Global attractor for a fractional nonlinear Klein-Gordon-Schrödinger system

Abstract We study the long time behaviour of the solutions for aweakly damped forced nonlinear fractional Klein-Gordon-Schrödinger system iut + iνu − (−∆)αu + vu − |u|2u = f, vtt+ γvt + (−∆)αv + v+ v3 − |u|2 = g, for a given α ∈(1/2, 1) considered in the whole space R. We prove that thissystem provides an infinite dimensional dynamical system in Hα(R) × Hα(R) × L2(R) that possesses a global attractor Aα in the same spaceand more particularly that this attractor is in fact a compact subset of H2α(R) × H2α(R) × Hα(R). Mathematics Subject Classification (2010). Primary 37L30,37L50; Secondary 35A01