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 -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!