From Boltzmann equation for granular gases to a modified Navier-Stokes-Fourier system - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Statistical Physics Année : 2022

From Boltzmann equation for granular gases to a modified Navier-Stokes-Fourier system

Résumé

In this paper, we give an overview of the results established in [3] which provides the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres in 3D. In particular, we obtain a new system of hydrodynamic equations describing granular flows and prove existence of classical solutions to the aforementioned system. One of the main issue is to identify the correct relation between the restitution coefficient (which quantifies the rate of energy loss at the microscopic level) and the Knudsen number which allows us to obtain non trivial hydrodynamic behavior. In such a regime, we construct strong solutions to the inelastic Boltzmann equation, near thermal equilibrium whose role is played by the so-called homogeneous cooling state. We prove then the uniform exponential stability with respect to the Knudsen number of such solutions, using a spectral analysis of the linearized problem combined with technical a priori nonlinear estimates. Finally, we prove that such solutions converge, in a specific weak sense, towards some hydrodynamic limit that depends on time and space variables only through macroscopic quantities that satisfy a suitable modification of the incompressible Navier-Stokes-Fourier system.
Fichier principal
Vignette du fichier
ALT-final.pdf (407.16 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03457897 , version 1 (30-11-2021)
hal-03457897 , version 2 (16-01-2023)

Identifiants

  • HAL Id : hal-03457897 , version 2

Citer

Ricardo J Alonso, Bertrand Lods, Isabelle Tristani. From Boltzmann equation for granular gases to a modified Navier-Stokes-Fourier system. Journal of Statistical Physics, 2022, 187 (3), Paper No. 28, 31 pp. ⟨hal-03457897v2⟩
38 Consultations
36 Téléchargements

Partager

Gmail Facebook X LinkedIn More