Existence of Global Weak Solutions for a 2D Viscous Shallow Water Equations and Convergence to the Quasi-Geostrophic Model

By Didier Bresch, B. Desjardins. 2003

526 citations recorded by the source corpus.

Subfields: Applied Mathematics, Earth-Surface Processes, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/04a6f6ee94ce0e9001ec6350a1e3816d609727e7

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In Applied Mathematics

In Earth-Surface Processes

In Mathematical Physics

Citations in the corpus

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].”
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.”
Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type (2009, unknown): “ut imposing that ρ∈ L2 loc, for this he introduces the concept of oscillation defect measure evaluating the lost of compactness. We can ﬁnally cite a very interesting result from Bresch-Desjardins in [5],[6] where they show the existence of global weak solution for (NHV) with κ= 0 in choosing speciﬁ”
On the Barotropic Compressible Navier–Stokes Equations (2007, methodology): “They showed the stability of weak solutions for the following Korteweg's system of equations: The result was later improved by Bresch and Desjardins ( 2003 ) to include the case of vanishing capillarity (κ = 0), but with an additional quadratic friction term r ρ | u | u (see also Bresch and Desj”
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).”
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.”
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.”
On the flow of chemically reacting gaseous mixture (2012, methodology): “This information is in a sense crucial, since it allows us to improve the information about density by repeating the Bresch–Desjardins entropy estimate.”
Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids (2010, background): “Indeed in [5] Bresch and Desjardins have discovered a new entropy inequality when in (1.”
On the existence of global weak solutions to the Navier–Stokes equations for viscous compressible and heat conducting fluids (2007, background): “A stability result on barotropic compressible Navier–Stokes equations is proved for general viscosities satisfying the constraint published in [7], assuming gamma type pressure law p(ρ) = ρ with γ ≥ 1, without adding friction forces as in the previous work of the authors on the shallow water model i”