Hilbert Expansion for Coulomb Collisional Kinetic Models
Analysis of PDEs
2023-06-08 v3
Abstract
The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau equation (r-LAN) are fundamental models that describe the dynamics of an electron gas. In this paper, we introduce a novel weighted energy method and establish the validity of the Hilbert expansion for the r-VML system and r-LAN equation. As the Knudsen number shrinks to zero, we rigorously demonstrate the relativistic Euler-Maxwell limit and relativistic Euler limit, respectively. This successfully resolves the long-standing open problem regarding the hydrodynamic limits of Landau-type equations.
Keywords
Cite
@article{arxiv.2207.00126,
title = {Hilbert Expansion for Coulomb Collisional Kinetic Models},
author = {Zhimeng Ouyang and Lei Wu and Qinghua Xiao},
journal= {arXiv preprint arXiv:2207.00126},
year = {2023}
}
Comments
52 pages; Typos corrected. arXiv admin note: text overlap with arXiv:2205.01483