Some applications of the method of moments for the homogeneous Boltzmann and Kac equations

Using the method of moments, we prove that any polynomial moment of the solution of the homogeneous Boltzmann equation with hard potentials or hard spheres is bounded provided that a moment of order strictly higher than 2 exists initially. We also give partial results of convergence towards the Maxwellian equilibrium in the case of soft potentials. Finally, exponential as well as Maxwellian estimates are introduced for the Kac equation.