Low Mach number limit around the planar diffusion wave for 3D Navier-Stokes-Fourier equations
Abstract
We investigate the low Mach number limit of the three-dimensional full compressible Navier-Stokes-Fourier (NSF) equations on ℝ×𝕋2 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 small independently of the Mach number and the non-zero modes of the initial perturbations are exponentially small. 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. The corresponding local-in-time result is proved while the difference between the states at the far fields can be arbitrarily large for the ill-prepared data.
Related
- Normal-Direction Energy and Fourier Restriction for Convex Planar Curves
- The exact number of nonconstant positive solutions to the planar isotropic Lp dual Minkowski problem
- A planar signed graph with circular chromatic number five
- The Class Edge-Reconstruction Number of a Maximal Planar Graph Is One or Two
- The Maximum Number of Halving Lines for Finite Planar Sets—New Lower Bounds
BibTeX
@misc{ju2026mach,
title = {{Low Mach number limit around the planar diffusion wave for 3D Navier-Stokes-Fourier equations}},
author = {Qiangchang Ju and Rui Li and Fanrui Meng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27281},
eprint = {2609.27281},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27281},
}
RIS
TY - UNPB
TI - Low Mach number limit around the planar diffusion wave for 3D Navier-Stokes-Fourier equations
AU - Qiangchang Ju
AU - Rui Li
AU - Fanrui Meng
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.27281
UR - https://arxiv.org/abs/2609.27281
AB - We investigate the low Mach number limit of the three-dimensional full compressible Navier-Stokes-Fourier (NSF) equations on ℝ×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 small independently of the Mach number and the non-zero modes of the initial perturbations are exponentially small. 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. The corresponding local-in-time result is proved while the difference between the states at the far fields can be arbitrarily large for the ill-prepared data.
ER -