Regularity theory for the spatially homogeneous Boltzmann equation with cut-off

Mouhot, Clément; Villani, Cédric

Mouhot, Clément; Villani, Cédric (2004), Regularity theory for the spatially homogeneous Boltzmann equation with cut-off, Archive for Rational Mechanics and Analysis, 173, 2, p. 169-212. http://dx.doi.org/10.1007/s00205-004-0316-7

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00087274/en/

Date

2004

Journal name

Archive for Rational Mechanics and Analysis

Volume

173

Number

Publisher

Springer-Verlag

Pages

169-212

Abstract (EN)

We develop the regularity theory of the spatially homogeneous Boltzmann equation with cut-off and hard potentials (for instance, hard spheres), by (i) revisiting the Lp-theory to obtain constructive bounds, (ii) establishing propagation of smoothness and singularities, (iii) obtaining estimates about the decay of the sin- gularities of the initial datum. Our proofs are based on a detailed study of the “regularity of the gain operator”. An application to the long-time behavior is presented.

Subjects / Keywords

Boltzmann equation ; spatially homogeneous ; hard spheres ; hard potentials ; angular cutoff ; regularity theory ; quantitative ; relaxation to equilibrium