Gevrey class regularity for the attractor of the laser equations

Constantin, Foais and Gibbon proved that the laser equations (Lorenz PDE) define a dynamical system in L-2 With a C-infinity attractor. We extend this theorem to show that the attractor is contained in every Gevrey class, G(s), for 1 < s < infinity. This demonstrates a remarkable smoothing mechanism for this hyperbolic system. We consider the consequences of this theorem for finite-dimensionality of the dynamics.