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., mu(rho)=A rho(theta), where A and theta are positive constants. New global existence result is established for 0 <theta < 1 when the initial density appears vacuum in the interior of the gas, which is the novelty of the presentation. (c) 2007 Elsevier Inc. All rights reserved.