The Shakhov model near a global Maxwellian. (April 2023)

• Record Type: Journal Article
• Authors: Bae, Gi-Chan; Yun, Seok-Bae
• Is Part Of: Nonlinear analysis. Volume 70(2023)
• Publication Date: 2023-04
• Subjects: Boltzmann equation -- BGK model -- Shakhov model -- Cauchy problem -- Asymptotic behavior -- Nonlinear energy method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103742
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Shakhov model is a relaxation approximation of the Boltzmann equation proposed to overcome the deficiency of the original BGK model, namely, the incorrect production of the Prandtl number. In this paper, we address the existence and the asymptotic stability of the Shakhov model when the initial data is a small perturbation of global equilibrium. We derive a dichotomy in the coercive estimate of the linearized relaxation operator between zero and non-zero Prandtl number, and observe that the linearized relaxation operator is more degenerate in the former case. To remove such degeneracy and recover the full coercivity, we consider a micro–macro system that involves an additional non-conservative quantity related to the heat flux.