COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY AND VACUUM

By Tong Yang, Zheng-an Yao, Changjiang Zhu. 2001

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Global Weak Solutions to 1D Compressible Isentropic Navier-Stokes Equations with Density-Dependent Viscosity (2005, methodology): “(2.3) can be shown easily by using the equation (1.4) and (2.2) while (2.4) follows from the multiplication of (1.5) with 2nu2n 1 in L2 and integration by parts, their proof can be found in [ 17 ].”
Compressible Navier–Stokes Equations with Degenerate Viscosity Coefficient and Vacuum (2002, methodology): “By using Helly’s theorem and arguments in one of the references [13, 14, 18–20, 24], we complete the proof of Theorem 2.”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, background): “And the global existence of weak solutions, together with α ∈ (0, 1) and the density function connecting to vacuum with discontinuities, was considered by many authors, see [23, 43, 55] and the references therein.”
Global Behavior of Compressible Navier-Stokes Equations with a Degenerate Viscosity Coefficient (2006, background): “Makino [14]; Okada [15]; Yang, Yao & Zhu [ 19 ]; Yang & Zhao [20]; Yang & Zhu [21]; Vong, Yang & Zhu [17] and Fang & Zhang [1‐5].”