Global existence of solutions for compressible Navier–Stokes equations with vacuum

In this paper, we will investigate the global existence of solutions for the one-dimensional compressible Navier–Stokes equations when the density is in contact with vacuum continuously.More precisely, the viscosity coefficient is assumed to be a power function of density, i.e., μ(ρ) = Aρθ, where A and θ are positive constants. New global existence result is established for 0 < θ <1 when the initial density appears vacuum in the interior of the gas, which is the novelty of the presentation. © 2007 Elsevier Inc. All rights reserved