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<p>For the general compressible 3<i>D</i> compressible Navier-Stokes-Fourier (NSF) equations, we establish local well-posedness for large data with no vacuum and global well-posedness for small perturbations of a stable constant equilibrium state. The main novelties of this paper are: (1) The NSF equations we study are fully general in the sense that we only assume the most basic thermodynamic conditions, i.e., the pressure and internal energy are monotone with respect to the density and temperature, respectively. (2) We fully employ the entropy structure and illustrate its role played in the analytical study of the compressible NSF.</p>

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On the Global Well-Posedness of the 3D Compressible Navier-Stokes-Fourier Equations with General Pressure Law

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  • 发表日期：

    2026年3月25日

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  • Yuhan Chen,
  • Guilong Gui,
  • Ning Jiang

摘要

For the general compressible 3D compressible Navier-Stokes-Fourier (NSF) equations, we establish local well-posedness for large data with no vacuum and global well-posedness for small perturbations of a stable constant equilibrium state. The main novelties of this paper are: (1) The NSF equations we study are fully general in the sense that we only assume the most basic thermodynamic conditions, i.e., the pressure and internal energy are monotone with respect to the density and temperature, respectively. (2) We fully employ the entropy structure and illustrate its role played in the analytical study of the compressible NSF.