On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation

In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from initial data and collision kernel is studied. Well-posedness long-time behavior – exponential decay to global equilibrium of analytical solution, spectral gap estimate for corresponding linearized gPC-based stochastic Galerkin system are obtained, by using extending tools provided in [M. Briant E.S. Daus, Arch. Ration. Mech. Anal. 3 (2016) 1367–1443] deterministic problem perturbative regime, [E.S. S. Jin L. Liu, Kinet. Relat. Models 12 (2019) 909–922] single-species uncertainty. The well-posedness result sensitivity presented here has not been obtained so far neither single species case nor case.