The Time Decay Estimate Of The Viscosity Dependence On The Density Of One-dimensional Compressible Navier-stokes Equations The Cauchy Problem Solution

We consider the following Cauchy problem for ID compressible flows with density-dependent viscosity coefficients:Hereρ(x, t) and u(x, t) stand for the fluid density and velocity respectively.γ≥l,and (?)≥0 are constants.In this paper,we are mainly concerned with the decay rate of the density and velocityas t�'∞. The contents of the paper include two parts:1. We consider the decay rate of the density and velocity as (?) > 0. We first obtain the decay rate ofρ-(?) and u in L~2(R) norm. Then we obtain the decay rate ofρ- (?)in L~∞(R) norm.2. We consider the decay rate of the density and velocity as (?) = 0. We construct a functional and use the energy method to obtain the decay rate ofρin L~∞(R) norm.