Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects

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Existence of global weak solutions for 3D degenerate compressible Navier–Stokes equations (2015, result): “[25] F. Marche, Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects.”
Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities (2015, background): “Recently, a friction shallow-water system, with flat bottom topography, which is derived in [5, 6, 9, 28], can be written in a two-dimensional space domain Ω as (1.”
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation* (2009, methodology): “zb u dz, it is well known [11,16,18,20] that the shallow water system (3.”
On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models (2006, background): “Let us emphasize that the stress tensor obtained from a formal derivation of the Saint–Venant model in 2d requires to deal with 2νhD(u)+2ν∇(hdivu), see [11], which at the moment cannot be treated by the present work.”