Low Mach number limit of the full Navier-Stokes equations with no-slip boundary conditions and large temperature variations
Abstract
In this paper, we rigorously justify the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional smooth bounded domain, subject to the no-slip boundary condition for the velocity and well-prepared initial data. In the presence of heat conduction and large temperature variations, we establish the uniform estimates for strong solutions on a time interval independent of the Mach number by constructing an energy functional in a Sobolev framework. The no-slip boundary condition cannot provide the vorticity boundary relation used in the slip-boundary setting. To overcome this difficulty, a divergence-free Stokes lifting of the boundary trace for the time derivative of the modified velocity is employed to define a test function vanishing on the boundary, which enables the transfer of a priori estimates from the velocity to the temperature.
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BibTeX
@misc{gu2026mach,
title = {{Low Mach number limit of the full Navier-Stokes equations with no-slip boundary conditions and large temperature variations}},
author = {Xiaoyu Gu and Song Jiang and Qiangchang Ju and Yaobin Ou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06567},
eprint = {2610.06567},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06567},
}
RIS
TY - UNPB
TI - Low Mach number limit of the full Navier-Stokes equations with no-slip boundary conditions and large temperature variations
AU - Xiaoyu Gu
AU - Song Jiang
AU - Qiangchang Ju
AU - Yaobin Ou
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.06567
UR - https://arxiv.org/abs/2610.06567
AB - In this paper, we rigorously justify the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional smooth bounded domain, subject to the no-slip boundary condition for the velocity and well-prepared initial data. In the presence of heat conduction and large temperature variations, we establish the uniform estimates for strong solutions on a time interval independent of the Mach number by constructing an energy functional in a Sobolev framework. The no-slip boundary condition cannot provide the vorticity boundary relation used in the slip-boundary setting. To overcome this difficulty, a divergence-free Stokes lifting of the boundary trace for the time derivative of the modified velocity is employed to define a test function vanishing on the boundary, which enables the transfer of a priori estimates from the velocity to the temperature.
ER -