Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (3): 1239-1250.doi: 10.1007/s10473-023-0314-1

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THE LOW MACH NUMBER LIMIT FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A REVISED MAXWELL'S LAW*

Yuxi Hu1, Zhao Wang2   

  1. 1. Department of Mathematics, China University of Mining, Technology, Beijing100083, China;
    2. Institute of Applied Physics, Computational Mathematics, Beijing100088, China
  • Received:2021-10-27 Revised:2022-08-04 Online:2023-06-25 Published:2023-06-06
  • About author:Yuxi Hu, E-mail: yxhu86@163.com; Zhao Wang, E-mail: wz_mi_hbu@yeah.net
  • Supported by:
    Yuxi HU was supported by the NNSFC (11701556) and the Yue Qi Young Scholar Project, China University of Mining and Technology (Beijing).

Abstract: We investigate the low Mach number limit for the isentropic compressible Navier-Stokes equations with a revised Maxwell's law (with Galilean invariance) in $\mathbb R^3$. By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.

Key words: isentropic compressible Navier-Stokes equations, low Mach number limit, revised Maxwell's law

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