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This paper concerns the existence of global weak solutions to the barotropiccompressible Navier-Stokes equations with degenerate viscosity coefficients. Weconstruct suitable approximate system which has smooth solutions satisfying theenergy inequality, the BD entropy one, and the Mellet-Vasseur type estimate.Then, after adapting the compactness results due to Mellet-Vasseur [Comm.Partial Differential Equations 32 (2007)], we obtain the global existence ofweak solutions to the barotropic compressible Navier-Stokes equations withdegenerate viscosity coefficients in two or three dimensional periodic domainsor whole space for large initial data. This, in particular, solved an openproblem in [P. L. Lions. Mathematical topics in fluid mechanics. Vol. 2.Compressible models. Oxford University Press, 1998].

Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities