About L-P estimates for the spatially homogeneous Boltzmann equation

Desvillettes, L; Mouhot, C

About L-P estimates for the spatially homogeneous Boltzmann equation

Accepted version

Peer-reviewed

Repository URI

https://www.repository.cam.ac.uk/handle/1810/275120

Repository DOI

https://doi.org/10.17863/CAM.22299

Files

Version of Record (165.21 KB)

Type

Article

Authors

Desvillettes, L

Mouhot, C

Abstract

For the homogeneous Boltzmann equation with (cutoff or non cutoff) hard potentials, we prove estimates of propagation of Lp norms with a weight $(1+| x |2) q / 2$ ( $1< p <+ \infty$ , $q ∈\R_+$ large enough), as well as appearance of such weights. The proof is based on some new functional inequalities for the collision operator, proven by elementary means.

Keywords

Boltzmann equation, propagation of L-P moments, appearance of L-P moments, angular singularity, noncutoff, ENTROPY DISSIPATION, EXISTENCE, RANGE, COMPACTNESS, REGULARITY, UNIQUENESS, CUTOFF, GAS

Journal Title

ANN I H POINCARE-AN

Journal ISSN

0294-1449
1873-1430

Volume Title

22

Publisher

European Mathematical Society - EMS - Publishing House GmbH

Publisher DOI

https://doi.org/10.1016/j.anihpc.2004.03.002

Rights

http://www.rioxx.net/licenses/all-rights-reserved

Collections

Scholarly Works - Pure Mathematics and Mathematical Statistics