About $L^p$ estimates for the spatially homogeneous Boltzmann equation

Desvillettes, Laurent; Mouhot, Clément

Desvillettes, Laurent; Mouhot, Clément (2005), About $L^p$ estimates for the spatially homogeneous Boltzmann equation, Annales de l'Institut Henri Poincaré. Analyse non linéaire, 22, 2, p. 127-142. http://dx.doi.org/10.1016/j.anihpc.2004.03.002

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00087260/en/

Date

2005

Journal name

Annales de l'Institut Henri Poincaré. Analyse non linéaire

Volume

Number

Publisher

Elsevier

Pages

127-142

Abstract (EN)

For the homogeneous Boltzmann equation with (cutoff or non cutoff ) hard potentials, we prove estimates of propagation of Lp norms with a weight $(1+ |x|^2)^q/2$ ($1 < p < +\infty$, $q \in \R_+$ 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.

Subjects / Keywords

integrability estimates; non-cutoff; spatially homogeneous; Boltzmann equation