%0 Journal Article %T The Compressible Navier-Stokes Equations with Weak Viscosity and Heat Conductivity %A Wan Zhang %A Hang Yang %A Liping Liu %J American Journal of Computational Mathematics %P 32-47 %@ 2161-1211 %D 2019 %I Scientific Research Publishing %R 10.4236/ajcm.2019.92003 %X
It is well known that the full compressible Navier-Stokes equations with viscosity and heat conductivity coefficients of order of the Knudsen number ¨°>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.
%K Compressible Navier-Stokes System %K Energy Estimate %K the Helmholtz Decomposition %K Elliptic Estimates %K the Galerkin Method %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=92680