A gradient flow approach to the Boltzmann equation
Analysis of PDEs
2023-06-14 v5
Abstract
We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which takes the collision process into account. This gradient flow structure allows to give a new proof for the convergence of Kac's random walk to the homogeneous Boltzmann equation, exploiting the stability of gradient flows.
Cite
@article{arxiv.1603.00540,
title = {A gradient flow approach to the Boltzmann equation},
author = {Matthias Erbar},
journal= {arXiv preprint arXiv:1603.00540},
year = {2023}
}
Comments
Final version as to appear in the journal. Modifications to previous version include generalisation of the main results to a class of soft potentials, discussion of generalised gradient structures for the Boltzmann equation