STABILITY AND EXPONENTIAL CONVERGENCE FOR THE BOLTZMANN-EQUATION

We prove existence, uniqueness and stability for solutions of the nonlinear Boltzmann equation in a periodic box in the case when the initial data are sufficiently close to a spatially homogeneous function. The results are given for a range of spaces, including L(1), and extend previous results in L(infinity) for the nonhomogeneous equation, as well as the more developed L(p)-theory for the spatially homogeneous Boltzmann equation. We also give new L(infinity)-estimates for the spatially homogeneous equation in the case of Maxwellian interactions.