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arXiv · 2609.22738

Incompressible Navier-Stokes Limit of the Relativistic Boltzmann Equation with the Optimal Convergence Rate

Yanchao Li·Mingying Zhong
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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 $\mathbf{c}.$

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Yanchao Li, Mingying Zhong. 2026-09-19. Incompressible Navier-Stokes Limit of the Relativistic Boltzmann Equation with the Optimal Convergence Rate. https://arxiv.org/abs/2609.22738

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