Hilbert expansion for Coulomb collisional kinetic models
Authors:
Zhimeng Ouyang, Lei Wu and Qinghua Xiao
Journal:
Quart. Appl. Math.
MSC (2020):
Primary 82C40; Secondary 76P05, 35Q20
DOI:
https://doi.org/10.1090/qam/1689
Published electronically:
March 12, 2024
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Additional Information
Abstract: The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau (r-LAN) equation 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 one-species 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.
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Additional Information
Zhimeng Ouyang
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637
MR Author ID:
1375691
ORCID:
0000-0002-5753-0278
Email:
zhimeng_ouyang@alumni.brown.edu
Lei Wu
Affiliation:
Department of Mathematics, Lehigh University, Bethlehem, PA 18015
ORCID:
0000-0002-7349-529X
Email:
lew218@lehigh.edu
Qinghua Xiao
Affiliation:
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China
Email:
xiaoqh@apm.ac.cn
Keywords:
Hilbert expansion,
relativistic Landau equation,
relativistic Vlasov-Maxwell-Landau system,
local Maxwellian
Received by editor(s):
August 31, 2023
Received by editor(s) in revised form:
February 11, 2024
Published electronically:
March 12, 2024
Additional Notes:
The first author was supported by an NSF Grant DMS-2202824. The second author was supported by an NSF Grant DMS-2104775. The third author was supported by NSFC Grants 11871469 and 12271506.
Article copyright:
© Copyright 2024
Brown University
