English

Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary

Analysis of PDEs 2024-01-08 v4

Abstract

In this short note, we prove an L6L^6-control of the macroscopic part of the linear Boltzmann and Landau equations. This result is an extension of the test function method of Esposito-Guo-Kim-Marra~\cite{EGKM}\cite{EGKM2} to the specular reflection boundary condition, in which we crucially used the Korn's inequality \cite{DV2} and the system of symmetric Poisson equations \cite{Bernou}.

Keywords

Cite

@article{arxiv.2307.11693,
  title  = {Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary},
  author = {Hongxu Chen and Chanwoo Kim},
  journal= {arXiv preprint arXiv:2307.11693},
  year   = {2024}
}