Open Access
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 R3.

Citation

Download Citation

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

Keywords: Absolute continuity , Besov spaces , Entropy , kinetic equations , regularization

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.25 • No. 2 • April 2015
Back to Top