Uniform L^p-Stability theory for the space-inhomogeneous Boltzmann equation with external forces

In this paper, we present an L^P-stability theory for the space-inhomogeneous Boltzmann equation with cut-off and inverse power law potentials, when initial data are sufficiently small and decay fast enough in phase space. For moderately soft potentials, we show that classical solutions depend Lipschitz continuously on the initial data in weighted L ^P-norm. In contrast for hard potentials, we show that classical solutions depend Holder continuously on the initial data. Our stability estimates are based on the dispersion estimates due to time-asymptotic linear Vlasov dynamics.