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.