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arXiv · 2602.07957

Relative entropy and slightly compressible Navier-Stokes dynamics of the Boltzmann equation

Yuhan Chen·Ning Jiang
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Abstract

This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain $\mathbb{T}^3$, using the relative entropy method originated from Bardos, Golse, Levermore [{\em Comm. Pure Appl. Math.} {\bf 46} (1993) 667--753] and Yau [{\em Lett. Math. Phys.} {\bf 22} (1991) 63--80]. We discuss the evolution of the entropy which is relative to the local Maxwellian governed by the solution of slightly compressible Navier-Stokes system. This characterizes the convergence rate from Boltzmann equation to the incompressible Navier-Stokes system.

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Yuhan Chen, Ning Jiang. 2026-02-08. Relative entropy and slightly compressible Navier-Stokes dynamics of the Boltzmann equation. https://arxiv.org/abs/2602.07957

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