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

Abstract : 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.
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Conference papers

https://hal-polytechnique.archives-ouvertes.fr/hal-01721097
Contributor : François Golse <>
Submitted on : Thursday, March 1, 2018 - 5:04:00 PM
Last modification on : Wednesday, October 14, 2020 - 4:21:47 AM

### Citation

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⟩

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