Global classical solution of the Cauchy problem to 1D compressible Navier-Stokes equations with large initial data

Abstract

In this paper, we prove that the 1D Cauchy problem of the compressible Navier-Stokes equations admits a unique global classical solution $(\rho,\rm u)$ if the viscosity $\mu(\rho)=1+\rho^{\beta}$ with $\beta\geq0$. The initial data can be arbitrarily large and may contain vacuum. Some new weighted estimates of the density and velocity are obtained when deriving higher order estimates of the solution.