Property Of The Solution To The Full Compressible Navier-Stokes Equations In The Half Space

In this paper, we investigate the initial value and the boundary value problem of nonlinear partial differential equations in the Eulerian coordinatesWhere u is the velocity, ρ is the density, θ(> 0) is the absolute temperature, u , ρ and θ(>0) is depended on time variable t and one-dimension variable x.μ(>0) is the viscosity constant, κ(>0) is the coefficient of heat conduction. The pressure p, the internal energy e and the thermodynamic entropy s are related to the density ρ and the absolute temperature θ by the equation of the state of the fluids. Defining v =1/ρ , the second law of thermodynamics asserts that de = θds - pdv and has that p = p(v,θ) = p(v, s), e = e(v,θ) = e(v, s) . In this...