Work

Long time asymptotic equivalence of the Vlasov-Poisson-Boltzmann equations at the level of the compressible Navier-Stokes-Poisson equations

Year: 2025

Type: article

Abstract: In this paper, we are concerned with long time asymptotic equivalence between the Vlasov-Poisson-Boltzmann (VPB) system and the compressible Navier-Stokes-Poisson (NSP) system. The density of the VPB system is proved to be asymptotically equivalent (mod decay rate $ (1+t)^{-1} $) as $ t\rightarrow \infty $ to that of the compressible Navier-Stokes-Poisson equations for the corresponding initial data. Regarding the momentum difference, we separately analyze the real and imaginary parts of its Fourier transform. It is shown that the real part decays at a rate of $ (1+t)^{-\frac{3}{4}}\ln(1+t) $, while the imaginary part decays at an optimal rate of $ (1+t)^{-\frac{1}{4}} $.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025050

Authors: Jiahuan Chen, Yachun Li

Institution: Shanghai Jiao Tong University

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: 一些双曲系统的动力学性态与机制, G459545773, G5291915726