The Boltzmann equation over $\mathbf{R}^D$: dispersion versus dissipation

François Golse (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

The Boltzmann equation of the kinetic theory of gases involves two competing processes. Dissipation (or entropy production) due to the collisions between gas molecules drives the gas towards local thermodynamic (Maxwellian) equilibrium. If the spatial domain is the Euclidean space $\mathbf{R}^D$, the ballistic transport of gas molecules between collisions results in a dispersion effect which enhances the rarefaction of the gas, and offsets the effect of dissipation. The competition between these two effects leads to a scattering regime for the Boltzmann equation over $\mathbf{R}^D$ with molecular interaction satisfying Grad's angular cutoff assumption. The present paper reports on results in this direction obtained in collaboration with Bardos, Gamba and Levermore [Comm. Math. Phys. 346 (2016), 435–467] and discusses a few open questions related to this work.

Keywords: Boltzmann equation; Global Maxwellian; Boltzmann collision integral; Boltzmann H Theorem; Free transport; Large time limit; Scattering operator

Domains: Analysis of PDEs [math.AP]

François Golse. The Boltzmann equation over $\mathbf{R}^D$: dispersion versus dissipation. From particle systems to partial differential equations III., Dec 2014, Braga, Portugal. ⟨10.1007/978-3-319-32144-8_7⟩. ⟨hal-01721097⟩