English

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

Analysis of PDEs 2016-08-16 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0607539,
  title  = {Regularity theory for the spatially homogeneous Boltzmann equation with cut-off},
  author = {Clément Mouhot and Cédric Villani},
  journal= {arXiv preprint arXiv:math/0607539},
  year   = {2016}
}

Comments

47 pages