BGK model for multi-component gases near a global Maxwellian

TL;DR

This paper proves the global existence and uniqueness of classical solutions for a multi-component BGK kinetic model near equilibrium, highlighting how inter-species interactions influence convergence rates.

Contribution

It establishes the first rigorous proof of global solutions for the multi-component BGK model with detailed analysis of dissipation mechanisms and convergence behavior.

Findings

Existence of unique global classical solutions near equilibrium.

Dissipation arises from combined intra- and inter-species relaxation operators.

Faster convergence when momentum-energy exchange rates increase.

Abstract

In this paper, we establish the existence of the unique global-in-time classical solutions to the multi-component BGK model suggested in \cite{mixmodel} when the initial data is a small perturbation of global equilibrium. For this, we carefully analyze the dissipative nature of the linearized multi-component relaxation operator, and observe that the partial dissipation from the intra-species and the inter-species 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.