Global classical solution to the 3D isentropic compressible Navier-Stokes equations with general initial data and a density-dependent viscosity coefficient

Abstract

In this paper, we study the global existence of classical solutions to the three-dimensional compressible Navier–Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). For the general initial data, which could be either vacuum or non-vacuum, we prove the global existence of classical solutions, under the assumption that the viscosity coefficient μ is large enough. Copyright © 2014 John Wiley & Sons, Ltd.