Energy method for the Boltzmann equation of monatomic gaseous mixtures

Abstract

In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Bolzmann equation around a global equilibrium is decomposed into the sum of a macroscopic and a microscopic part, for which we obtain a priori estimates at both lower and higher orders. These estimates are obtained under a suitable smallness assumption.The assumption can be justified a posteriori in the higher-order case, leading to the closure of the corresponding estimate.

BGK model for multi-component gases near a global Maxwellian

“…In [32], the existence and uniqueness are constructed in spatially homogeneous settings when an initial data has upper and lower bounds for some polynomial moments. The authors in [15] obtained some energy estimates.…”