Stability of background perturbation for Boltzmann equation
Analysis of PDEs
2023-08-01 v1
Abstract
Consider the Boltzmann equation in the perturbation regime. Since the macroscopic quantities in the background global Maxwellian are obtained through measurements, there are typically some errors involved. This paper investigates the effect of background variations on the solution for a given initial perturbation. Our findings demonstrate that the solution changes continuously with variations in the background and provide a sharp time decay estimate of the associated errors. The proof relies on refined estimates for the linearized solution operator and a proper decomposition of the nonlinear solution.
Keywords
Cite
@article{arxiv.2307.15849,
title = {Stability of background perturbation for Boltzmann equation},
author = {Yu-Chu Lin and Haitao Wang and Kung-Chien Wu},
journal= {arXiv preprint arXiv:2307.15849},
year = {2023}
}