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arXiv · 2609.27281

Low Mach number limit around the planar diffusion wave for 3D Navier-Stokes-Fourier equations

Qiangchang Ju·Rui Li·Fanrui Meng
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Abstract

We investigate the low Mach number limit of the three-dimensional full compressible Navier-Stokes-Fourier (NSF) equations on $\mathbb{R}\times\mathbb{T}^2$ for two different classes of initial data, corresponding respectively to a well-prepared regime and an ill-prepared regime. The density and temperature are allowed to approach different asymptotic states at infinity. For the well-prepared regime, the solutions of compressible NSF equations converge to a planar diffusion wave solution globally in time as the Mach number tends to zero, where the difference between the states at the far fields is independent of the Mach number. Moreover, the optimal time-decay rate can be obtained. It can be viewed as the first global-in-time result on the low Mach number limit of three-dimensional NSF equations with large temperature variations. For the ill-prepared regime, the corresponding local-in-time result is obtained by performing separate energy estimates for the zero and non-zero modes, and an auxiliary convergence lemma proposed by Métivier-Schochet in \cite{Métivier2001}. It is remarked that the difference between the states at the far fields is allowed to be arbitrarily large.

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Qiangchang Ju, Rui Li, Fanrui Meng. 2026-09-23. Low Mach number limit around the planar diffusion wave for 3D Navier-Stokes-Fourier equations. https://arxiv.org/abs/2609.27281

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