Regularity of the attractor for a fractional Klein-Gordon-Schrodinger system with cubic nonlinearities

We study the long time behavior of the solutions for a weakly damped forced nonlinear fractional Klein-Gordon-Schrodinger system iu(t) + ivu + i|u|(2)u - (-Delta)alpha u + vu =f, v(tt) + gamma v(t) - Delta v + v + v(3) - |u|(2) = g, for a given alpha epsilon (1/2, 1) considered in thewhole space R. We prove that this system provides an infinite dimensional dynamical system in H-alpha (R) x H-1(R) x L-2(R) that possesses a global attractor... in the same space andmore particularly that this attractor is in fact a compact set of H-2 alpha (R) x H1+alpha (R) x H-alpha (R).