Global Weak Solutions to 1D Compressible Isentropic Navier-Stokes Equations with Density-Dependent Viscosity

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On the flow of chemically reacting gaseous mixture (2012, background): “If the flow is isentrpoic, this dependence may be translated into the dependence on the density μ(%) = %(γ−1)/2, see [15], [10].”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, methodology): “By the standard arguments (see [17] for reference), after applying the classical theory of parabolic and hyperbolic equations, one can obtain that there exists some T∗ > 0 such that the approximate problem (3.”
On the existence of global weak solutions to the Navier–Stokes equations for viscous compressible and heat conducting fluids (2007, background): “Note that global existence of weak solutions in 1D with degenerate viscous term for compressible Navier-Stokes equations has been extensively studied, see for instance [44], [36] and [58] for an overview.”