Hypocoercivity for a BGK model for gas mixtures

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Liu, Liu¹  Pirner, Marlies² 

[1] Univ Texas Austin, ICES, 201 E 24th St, Austin, TX 78712 USA

[2] Univ Vienna, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

关键词: Kinetic equations;    BGK models;    Gas mixtures;    Hypocoercivity;    Large-time behavior;    Lyapunov functionals;   

DOI  :  10.1016/j.jde.2019.01.006

来源: Elsevier

【 摘 要 】

We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we can prove exponential relaxation to equilibrium with explicit rates. Our strategy is based on the entropy and spectral methods adapting Lyapunov's direct method as presented in [1] for the one species linearized BGK model. In comparison to the one species case, we start with two partial differential equations, one for each species. These equations are coupled due to interspecies interactions, which requires additional estimates on these interspecies terms. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free