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

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
2
Publisher
Springer-Verlag
Pages
169-212
Publication identifier
http://dx.doi.org/10.1007/s00205-004-0316-7
Metadata
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Author(s)
Mouhot, Clément
Villani, Cédric
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

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