On the existence of global weak solutions to the Navier–Stokes equations for viscous compressible and heat conducting fluids

By Didier Bresch, B. Desjardins. 2007

295 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/c82919ca5f302a49d13dbcc6ff6c2f1490ac032b

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In Applied Mathematics

In Computational Mechanics

In Control and Systems Engineering

Citations in the corpus

A Global Existence Result for the Compressible Navier–Stokes Equations in the Critical Lp Framework (2010, background): “Although the problem of global well-posedness for large data has remained unsolved, global ﬁnite energy weak solutions have been built by P.-L. Lions in [20] (see also the recent work by D. Bresch and B. Desjardins in [3] for the construction of global weak solutions with H 1 density).”
Global existence of weak solutions for compressible Navier--Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor (2015, background): “The almost only successful insight in this case can be found in [15, 16, 17, 64, 48] with no dependency with respect 16”
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.”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, methodology): “More recently, Bresch and Desjardins [2,3, 6 ,7] (see also [38]) have made important progress.”
Weak–Strong Uniqueness Property for the Full Navier–Stokes–Fourier System (2011, background): “More recently, Lions [21] extended the theory to the class of barotropic flows (see also [12]), and, finally, the existence of global-in-time generalized solutions for the full Navier-Stokes-Fourier system was proved in [12], [14, Chapter III] (see also Bresch and Desjardins [2], [3] for an altrenat”
On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models (2006, methodology): “The global existence of weak solutions is obtained by taking the limit ε → 0 and using the stability arguments detailed in [5] and [7].”
On the Barotropic Compressible Navier–Stokes Equations (2007, methodology): “Our result is in the same spirit as the one of Bresch, Desjardins and Lin and makes use of the same mathematical entropy, first discovered by Bresch and Desjardins ( 2002 ) for the particular case where h (ρ) = ρ and g (ρ) = 0, and later generalized by Bresch and Desjardins ( 2004 ) to include the”
Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type (2009, unknown): “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 specific type of viscosity where � and λ are linked.”
Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier–Stokes System with Vacuum and Large Oscillations (2011, background): “Recently, for a very particular form of the viscosity coefficients depending on the density, Bresch–Desjardins [3] obtained global stability of weak solutions.”