BGK model for two-component gases near a global Maxwellian

Bae, Gi-Chan; Klingenberg, Christian; Pirner, Marlies; Yun, Seok-Bae

Abstract

In this paper, we establish the existence of the unique global-in-time classical solutions to the two-component Bhatnagar–Gross–Krook (BGK) model suggested in [C. Klingenberg, M. Pirner, and G. Puppo, Kinet. Relat. Models, 10 (2017), pp. 445–465] when the initial data is a small perturbation of global equilibrium. For this, we carefully analyze the dissipative nature of the linearized two-component relaxation operator and observe that the partial dissipation from the intraspecies and the interspecies linearized relaxation operators are combined in a complementary manner to give rise to the desired dissipation estimate of the model. We also observe that the convergence rate of the distribution function increases as the momentum-energy interchange rate between the different components of the gas increases.