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.
Publié le : 2004-07-05
Classification:
Boltzmann equation,
spatially homogeneous,
hard spheres,
hard potentials,
angular cutoff,
regularity theory,
quantitative,
relaxation to equilibrium,
76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00087274,
author = {Mouhot, Cl\'ement and Villani, C\'edric},
title = {Regularity theory for the spatially homogeneous Boltzmann equation with cut-off},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00087274}
}
Mouhot, Clément; Villani, Cédric. Regularity theory for the spatially homogeneous Boltzmann equation with cut-off. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00087274/