From the Boltzmann equation to the Stokes‐Fourier system in a bounded domain

By Nader Masmoudi, Laure Saint-Raymond. 2003

160 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d090769b5cdea8dc3c7c02b33eda9dfef4277393

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

On the Inviscid Limit for the Compressible Navier–Stokes System in an Impermeable Bounded Domain (2012, unknown): “As in these works Theorem 4 fails to tackle the case where β is a O(1) when ε converges to 0, which seems of special interest in view of the kinetic derivation of the Navier condition performed in [27, 2].”
Boltzmann diffusive limit beyond the Navier‐Stokes approximation (2006, background): “To overcome such a mathematical difficulty, there have been many important contributions over the years [3, 14, 27, 28, 30, 31], among others.”
Decay and Continuity of the Boltzmann Equation in Bounded Domains (2008, background): “ce, there have been many contributions in the mathematical study of diﬀerent aspects of the Boltzmann boundary value problems [A], [AC], [AEMN], [AEP], [AH], [C2], [C3], [CC], [De], [Gui], [H], [LY], [MS], [M], [US], [YZ], among others, see also references in the books [C1], [CIP] and [U1]. Accordin”
Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition (2010, methodology): “This type of boundary condition is often used to model rough boundaries, we refer for example to [3], [8] (see also [28] for a derivation from the Maxwell boundary condition of the Boltzmann equation through a hydrodynamic limit).”
Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws (2015, methodology): “Applications of the relative entropy method in this context began with the work of Yau [55] and have been studied in various context (See for instance [2, 3, 7, 8, 23, 26, 34, 37, 38, 42]).”
Viscous boundary layers for the Navier–Stokes equations with the Navier slip conditions (2011, methodology): “More recently, Masmoudi and Saint-Raymond [ 30 ] derived some Navier conditions for the close Stokes‐ Fourier system from Maxwell conditions (combining perfect/specular reflection and diffuse/Gaussian reflection) for the Boltzmann equations.”
Hydrodynamic limit for the Vlasov-Navier-Stokes equations. Part I: Light particles regime (2004, result): “We mention with this respect the recent work by Masmoudi-Saint Raymond [22] about the Stokes limit from the Boltzmann equation.”
Stability and Asymptotic Analysis of a Fluid-Particle Interaction Model (2006, methodology): “We refer to [39, 7] for similar considerations and rigorous proofs in a different physical context.”
Relative Entropy and the Stability of Shocks and Contact Discontinuities for Systems of Conservation Laws with non-BV Perturbations (2010, unknown): “[20, 36, 31, 35].”
The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels (2004, methodology): “This problem can certainly be solved by the methods presented in this paper combined with those developed by N. Masmoudi and L. Saint-Raymond in [ 52 ].”