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 (ρ,u) if the viscosity μ(ρ)=1+ρβ with β⩾0. 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.