English

Boltzmann to Landau from the Gradient Flow Perspective

Analysis of PDEs 2022-02-03 v2

Abstract

We revisit the grazing collision limit connecting the Boltzmann equation to the Landau(-Fokker-Planck) equation from their recent reinterpretations as gradient flows. Our results are in the same spirit as the Γ\Gamma-convergence of gradient flows technique introduced by Sandier and Serfaty. In this setting, the grazing collision limit reduces to showing the lower semi-continuous convergence of the Boltzmann entropy-dissipation to the Landau entropy-dissipation.

Keywords

Cite

@article{arxiv.2107.07252,
  title  = {Boltzmann to Landau from the Gradient Flow Perspective},
  author = {José Carrillo and Matias Delgadino and Jeremy Wu},
  journal= {arXiv preprint arXiv:2107.07252},
  year   = {2022}
}

Comments

41.5 pages without references, 4 figures. Comparisons with other weak solutions have been expanded. Typos fixed and more clarifications added. Accepted version. Comments welcome!

R2 v1 2026-06-24T04:13:31.109Z