On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models

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On the flow of chemically reacting gaseous mixture (2012, background): “The basic idea is contained already in the work [3] and consists of introducing the smoothing operator δ ∇(μ′( ) 2s+1μ( )) with s sufficiently large, inspired from the capillarity forces [5].”
Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type (2009, unknown): “Indeed it allows to get enough compactness on the density to treat the temperature equation (see for more details [ 7 ,8,22]).”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, background): “. Thus, the blowup phenomena (2.42) happens. The proof of the Theorem 2.4 is completed. Acknowledgements The authors would like to thank the referee for informing them the recent published references [4,5,39] and the helpful comments on the manuscript. They also would like to thank Prof. Didier Bres”
Existence of global weak solutions for 3D degenerate compressible Navier–Stokes equations (2015, methodology): “The result was later extended for the case with an additional quadratic friction term rρ|u|u, refer to Bresch-Desjardins [2, 3] and the recent results by Bresch-Desjardins-Zatorska [5] and by Zatorska [35].”