On the asymptotic dynamics of the Vlasov-Yukawa-Boltzmann system near vacuum

In this paper, we study uniform L¹-stability and asymptotic completeness of the Vlasov-Yukawa-Boltzmann (V-Y-B) system. For a sufficiently small and smooth initial data, we show that classical solutions exist globally and satisfy dispersion estimates, uniform L¹-stability with respect to initial data and scattering type estimate. We show that the short range nature of interactions due to the Yukawa potential enables us to construct robust Lyapunov type functional to derive scattering states. In the zero mass limit of force carrier particles, we also show that the classical solutions to the V-Y-B system converge to that of the Vlasov-Poisson-Boltzmann (V-P-B) system in any finite time interval.