Propagation of Gevrey regularity for solutions of the Boltzmann equation   for Maxwellian molecules
  We prove that Gevrey regularity is propagated by the Boltzmann equation with Maxwellian molecules, with or without angular cut-off. The proof relies on the Wild expansion of the solution to the equation and on the characterization of Gevrey regularity by the Fourier transform. 
L. Desvillettes, G. Furioli, E. Terraneo