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Incompressible Navier-Stokes Limit of the Relativistic Boltzmann Equation with the Optimal Convergence Rate
Abstract
We study the diffusion limit of the classical solution to the relativistic Boltzmann equation with the initial data near a global relativistic Maxwellian. By using spectral analysis, we establish the convergence of the classical solution to the relativistic Boltzmann equation to that of the incompressible Navier-Stokes system, and give for the first time the optimal convergence rate and a precise estimate of the initial layer. Moreover, through a refined analysis of the linear collision operator L, combined with Duhamel's principle, we obtain the existence and uniqueness of a global strong solution to the relativistic Boltzmann equation, as well as a convergence rate independent of the speed of light c.
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BibTeX
@misc{li2026incompressible,
title = {{Incompressible Navier-Stokes Limit of the Relativistic Boltzmann Equation with the Optimal Convergence Rate}},
author = {Yanchao Li and Mingying Zhong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22738},
eprint = {2609.22738},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22738},
}
RIS
TY - UNPB
TI - Incompressible Navier-Stokes Limit of the Relativistic Boltzmann Equation with the Optimal Convergence Rate
AU - Yanchao Li
AU - Mingying Zhong
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22738
UR - https://arxiv.org/abs/2609.22738
AB - We study the diffusion limit of the classical solution to the relativistic Boltzmann equation with the initial data near a global relativistic Maxwellian. By using spectral analysis, we establish the convergence of the classical solution to the relativistic Boltzmann equation to that of the incompressible Navier-Stokes system, and give for the first time the optimal convergence rate and a precise estimate of the initial layer. Moreover, through a refined analysis of the linear collision operator L, combined with Duhamel's principle, we obtain the existence and uniqueness of a global strong solution to the relativistic Boltzmann equation, as well as a convergence rate independent of the speed of light c.
ER -