On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems

By Didier Bresch, B. Desjardins, Chi-Kun Lin. 2003

536 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/c94e51253dded0b62674ced9401be777a27afdbc

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In Applied Mathematics

In Computational Mechanics

In Materials Chemistry

Citations in the corpus

Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, background): “More recently, $Bre8ch\bm{t}d$ Daejardins $[1,2]$ (see also [15]) have made important progress.”
Existence and time-asymptotics of global strong solutions to dynamic Korteweg models (2014, background): “In [9], Bresch, Desjardins, and Lin obtained existence of global weak solutions in a periodic or strip domain without any smallness assumption on the initial data.”
On the flow of chemically reacting gaseous mixture (2012, background): “This property was observed for the first time by Bresch, Desjardins & Lin [5] for the Korteweg equations and for the 2-dimensional viscous shallow water model [2].”
Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects (2007, background): “As emphasized in [ 8 ] and [9], the introduction of the third-order surface-tension term induced by capillary effects and of the quadratic bottom friction term is of a great utility in the proof of existence of weak-solutions for this particular model.”
On the uniqueness of strong solution to the incompressible Navier–Stokes equations with damping (2011, unknown): “The damping is from the resistance to the motion of the flow, to which various physical phenomena such as porous media flow, drag or friction effects are related (see [2,3,9,10] and references therein).”
Existence of Global Weak Solutions for a 2D Viscous Shallow Water Equations and Convergence to the Quasi-Geostrophic Model (2003, methodology): “Moreover the diffusive tensor h∇u may be replaced by hD(u), where D(u) = (∇u + t ∇u)/2 without extra difficulties, see [ 3 ].”
On the Barotropic Compressible Navier–Stokes Equations (2007, unknown): “The first result handling this difficulty is due to Bresch et al. (2003). They showed the stability of weak solutions for the following Korteweg’s system of equations: t + div u = 0 t u + div u⊗ u + xp− div D u = (3)”
On the existence of global weak solutions to the Navier–Stokes equations for viscous compressible and heat conducting fluids (2007, methodology): “This assumption has recently been removed in [47] by assuming more integrability on the initial velocity than the only physically relevant bound, still using the structure discovered in [11].”
Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities (2015, background): “Moreover, they [1,2,4] also obtained the global existence of weak solutions to (1.”