On the Barotropic Compressible Navier–Stokes Equations

By Antoine Mellet, Alexis Vasseur. 2007

314 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b49e577f1774d75dce7c3344ea844a3bffbb9e67

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Global existence of solutions for the coupled Vlasov and Navier-Stokes equations (2009, background): “In [13], Mellet and Vasseur proved the existence of global weak solutions to the coupled Vlasov-Fokker-Planck and compressible Navier-Stokes equations (hence, including diffusive effects for the particles and compressibility effects for the fluid), for absorption or reflection boundary conditions, a”
Existence of global weak solutions for 3D degenerate compressible Navier–Stokes equations (2015, methodology): “Approximation of the Mellet-Vasseur type inequality In this section, we construct an approximation of the Mellet-Vasseur type inequality for any weak solutions at the following level of approximation system ρt + div(ρu) = 0, (ρu)t + div(ρu⊗ u) +∇ργ − div(ρDu) = −r0u− r1ρ|u|2u+ κρ∇( ∆ √ ρ √ ρ ), (2.1”
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 ]).”
On the flow of chemically reacting gaseous mixture (2012, background): “[19] A. Mellet, A. Vasseur, On the barotropic compressible Navier–Stokes equations, Comm. Partial Differential Equations 32 (1–3) (2007) 431–452.”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, methodology): “More recently, $Bre8ch\bm{t}d$ Daejardins $[1,2]$ (see also [15]) have made important progress.”