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2016 | OriginalPaper | Chapter

The Boltzmann Equation over \({{\mathbb R}^{{\mathrm {D}}}}\): Dispersion Versus Dissipation

Author : François Golse

Published in: From Particle Systems to Partial Differential Equations III

Publisher: Springer International Publishing

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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 \({{\mathbb R}^{{\mathrm {D}}}}\), 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 \({{\mathbb R}^{{\mathrm {D}}}}\) 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 [arxiv:1409.1430] and discusses a few open questions related to this work.

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previous chapter Entropy Dissipation Estimates for the Landau Equation: General Cross Sections

next chapter The Gradient Flow Approach to Hydrodynamic Limits for the Simple Exclusion Process

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Title: The Boltzmann Equation over : Dispersion Versus Dissipation
Author: François Golse
Publisher: Springer International Publishing
Book: From Particle Systems to Partial Differential Equations III
Print ISBN: 978-3-319-32142-4

Electronic ISBN: 978-3-319-32144-8

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-32144-8_7

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