Global well-posedness and large-time behavior of 1D compressible Navier-Stokes equations with density-depending viscosity and vacuum in unbounded domains (Q2037541)

The authors study the Cauchy problem for one dimensional barotropic compressible Navier Stokes equations with density depending viscosity and large external forces. Under a general assumption on the density-depending viscosity they prove that the Cauchy problem admits a unique global strong solution for large initial data with vacuum. Moreover, the density is proved to be bounded from above time independently. They also obtain the large time behavior of the solution without external forces