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April 2015 Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition
Nicolas Fournier
Ann. Appl. Probab. 25(2): 860-897 (April 2015). DOI: 10.1214/14-AAP1012

Abstract

We consider the $3D$ spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We assume that the initial condition is a probability measure with finite energy and is not a Dirac mass. For hard potentials, we prove that any reasonable weak solution immediately belongs to some Besov space. For moderately soft potentials, we assume additionally that the initial condition has a moment of sufficiently high order ($8$ is enough) and prove the existence of a solution that immediately belongs to some Besov space. The considered solutions thus instantaneously become functions with a finite entropy. We also prove that in any case, any weak solution is immediately supported by $\mathbb{R}^{3}$.

Citation

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Nicolas Fournier. "Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition." Ann. Appl. Probab. 25 (2) 860 - 897, April 2015. https://doi.org/10.1214/14-AAP1012

Information

Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1322.82013
MathSciNet: MR3313757
Digital Object Identifier: 10.1214/14-AAP1012

Subjects:
Primary: 60H30, 60J75, 82C40

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 2015
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