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 $(\rho ,\mathrm{u})$ if the viscosity $\mu (\rho )=1+{\rho }^{\beta }$ with $\beta \ge 0$. 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.

References in corpus (3)

• Global Well-Posedness of Classical Solutions to the Cauchy problem of Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data
• Global classical solutions to the two-dimensional compressible Navier-Stokes equations in ${\mathbb{R}}^2$
• Global well-posedness of 2D compressible Navier-Stokes equations with large data and vacuum