Global Solutions of the Boltzmann Equation Over RD Near Global Maxwellians with Small Mass

Claude Bardos; Irene M. Gamba; François Golse; C. David Levermore

doi:10.1007/s00220-016-2687-7

Global Solutions of the Boltzmann Equation Over R^D Near Global Maxwellians with Small Mass

Claude Bardos, Irene M. Gamba, François Golse, C. David Levermore

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Abstract

We study the dynamics defined by the Boltzmann equation set in the Euclidean space R^D in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As a result, the large time limit of solutions of the Boltzmann equation in this regime is given by noninteracting, freely transported states and can be described with the tools of scattering theory.

Original language	English
Pages (from-to)	435-467
Number of pages	33
Journal	Communications in Mathematical Physics
Volume	346
Issue number	2
DOIs	https://doi.org/10.1007/s00220-016-2687-7
Publication status	Published - 1 Sept 2016

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title = "Global Solutions of the Boltzmann Equation Over RD Near Global Maxwellians with Small Mass",

abstract = "We study the dynamics defined by the Boltzmann equation set in the Euclidean space RD in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As a result, the large time limit of solutions of the Boltzmann equation in this regime is given by noninteracting, freely transported states and can be described with the tools of scattering theory.",

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AU - Gamba, Irene M.

AU - Golse, François

AU - Levermore, C. David

PY - 2016/9/1

Y1 - 2016/9/1

N2 - We study the dynamics defined by the Boltzmann equation set in the Euclidean space RD in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As a result, the large time limit of solutions of the Boltzmann equation in this regime is given by noninteracting, freely transported states and can be described with the tools of scattering theory.

AB - We study the dynamics defined by the Boltzmann equation set in the Euclidean space RD in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As a result, the large time limit of solutions of the Boltzmann equation in this regime is given by noninteracting, freely transported states and can be described with the tools of scattering theory.

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VL - 346

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EP - 467

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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Global Solutions of the Boltzmann Equation Over RD Near Global Maxwellians with Small Mass

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Global Solutions of the Boltzmann Equation Over R^D Near Global Maxwellians with Small Mass