Conditional $L^{\infty}$ estimates for the non-cutoff Boltzmann equation in a bounded domain
Analysis of PDEs
2023-05-05 v1
Abstract
We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy and entropy densities are bounded above, and the mass density is bounded away from vacuum, we obtain an estimate of the norm of the solution depending on the macroscopic bounds on these hydrodynamic quantities only. It is a regularization effect in the sense that the initial data is not required to be bounded.
Cite
@article{arxiv.2305.02392,
title = {Conditional $L^{\infty}$ estimates for the non-cutoff Boltzmann equation in a bounded domain},
author = {Zhimeng Ouyang and Luis Silvestre},
journal= {arXiv preprint arXiv:2305.02392},
year = {2023}
}