The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels

By François Golse, Laure Saint-Raymond. 2004

327 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/f62a0c6e83a5cdb274227e245fc37a88d45ebfcd

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Asymptotic Analysis for a Vlasov-Fokker-Planck/ Compressible Navier-Stokes System of Equations (2008, methodology): “It is the main tool also for the asymptotic limit of the Boltzmann equation to the incompressible NavierStokes equation, see Bardos, Golse, Levermore [4], Golse, Saint-Raymond [14], Lions, Masmoudi [19].”
Boltzmann diffusive limit beyond the Navier‐Stokes approximation (2006, background): “Finally, in [15], a complete proof for such a limit was established for certain classes of collision kernels.”
Relative Entropy and the Stability of Shocks and Contact Discontinuities for Systems of Conservation Laws with non-BV Perturbations (2010, unknown): “[20,32,36,37].”
Numerical methods for kinetic equations* (2014, unknown): “We refer to Levermore (1996) for a mathematical setting of the problem and to Golse and Saint-Raymond (2004) for recent theoretical results.”
Convex integration and phenomenologies in turbulence (2019, methodology): “The Navier-Stokes equations may be derived rigorously from the Boltzmann equation [3, 134, 91], or from lattice gas models [163].”
Global existence for the Euler-Maxwell system (2011, background): “We refer to [23, 16, 21] for more about hydrodynamic limits.”
Euler equations for incompressible ideal fluids (2007, methodology): “In particular, it was ultimately shown by Golse and Saint-Raymond [45] that, modulo the extraction of a subsequence and for a suitable choice of space-time scaling, any sequence of such renormalized solutions of the Boltzmann equations converges (in some weak sense) to a Leray–Hopf solution of the N”
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation (2005, background): “incompressible limit, see [6, 40, 29 ] or the survey in [56].”
Moment Closure—A Brief Review (2015, background): “Taking a larger moment space M one may also get the Navier-Stokes equation as a limit [93], and this hydrodynamic limit can even be justified rigorously under certain assumptions [51].”
Asymptotic analysis of the lattice Boltzmann equation (2005, methodology): “[43]), is well known in kinetic theory and has been used to establish a direct connection between the Boltzmann equation and the incompressible Navier–Stokes equations [9,1,29,14,15].”
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]).”