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) = A ρθ, 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.
Qin, X., Yao, Z. an, & Zhou, W. (2008). Global existence of solutions for compressible Navier-Stokes equations with vacuum. Journal of Mathematical Analysis and Applications, 340(1), 226–238. https://doi.org/10.1016/j.jmaa.2007.08.033