Duan, R.-J., Liu, H.-X., Ukai, S. and Yang, T. (2007) Optimal Convergence Rates for the Compressible Navier-Stokes Equations with Potential Force. Journal of Differential Equations, 238, 220-233. https://doi.org/10.1016/j.jde.2007.03.008

has been cited by the following article:

• TITLE: The Compressible Navier-Stokes Equations with Weak Viscosity and Heat Conductivity

  AUTHORS: Wan Zhang, Hang Yang, Liping Liu

  KEYWORDS: Compressible Navier-Stokes System, Energy Estimate, the Helmholtz Decomposition, Elliptic Estimates, the Galerkin Method

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.9 No.2, May 27, 2019

  ABSTRACT: It is well known that the full compressible Navier-Stokes equations with viscosity and heat conductivity coefficients of order of the Knudsen number ò>0 can be deduced from the Boltzmann equation via the Chapman-Enskog expansion. In this paper, we carry out the rigorous mathematical study of the compressible Navier-Stokes equation with the initial-boundary value problems. We construct the existence and most importantly obtain the higher regularities of the solutions of the full compressible Navier-Stokes system with weak viscosity and heat conductivity in a general bounded domain.