convergence of the vlasov-poisson system to the incompressible euler equations

By Yann Brenier. 2000

318 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/3af79b8987e357c518dc265067cec2b29be4980a

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In Applied Mathematics

In Astronomy and Astrophysics

In Computational Mechanics

Citations in the corpus

Hamiltonian ODEs in the Wasserstein space of probability measures (2008, background): “…along any solution of our evolutive system: H(µt) = H(µ0). c© 2000 Wiley Periodicals, Inc. 1 Introduction In the last few years there has been a considerable interest in the theory of gradient flows in the Wasserstein spaceP2(RD) of probability measures with finite quadratic moments inRD,…”
Weak-Strong Uniqueness for Measure-Valued Solutions (2009, methodology): “This paper has been inspired by the works of Brenier and Grenier [3, 4].”
Mathematical tools for kinetic equations (2004, methodology): “(iii) strong electric field in Vlasov-Poisson system with a background; see Grenier [71] and Brenier [28] for a method based on modulated hamiltonians.”
RELATIVE ENTROPY IN HYPERBOLIC RELAXATION (2005, methodology): “This notion, introduced in the theory of conservation laws in [9, 11], has recently been applied to a variety of models; see [3], [2], [14] and [4], [1], [14, Thm 4.”
Asymptotic Analysis for a Vlasov-Fokker-Planck/ Compressible Navier-Stokes System of Equations (2008, methodology): “For different asymptotic problems it is called ”modulated energy” method (Brenier [10], [9]).”
Landau Damping: Paraproducts and Gevrey Regularity (2013, background): “One can also derive the incompressible Euler system from the Vlasov-Poisson system in the quasi-neutral regime for cold electrons (vanishing initial temperature) [18,60].”
Incompressible Limit of the Compressible Magnetohydrodynamic Equations with Periodic Boundary Conditions (2009, methodology): “The proof of Theorem 2.3 is based on the combination of the modulated energy method, motivated by Brenier [1], the weak convergence method and the refined energy analysis.”
The Convergence of the Navier–Stokes–Poisson System to the Incompressible Euler Equations (2006, methodology): “In particular, the limit → 0 has been performed in Vlasov-Poisson system by Brenier (2000), Grenier (1995, 1996, 1997a), and Masmoudi (2001a), in Schrödinger-Poisson system by Puel (2000) and Jüngel and Wang (2003), in drift-diffusion-Poisson system by Gasser et al. (2001, 2002), Jüngel and Peng…”
Hydrodynamic limit for the Vlasov-Navier-Stokes equations. Part I: Light particles regime (2004, methodology): “It has been successfully used to derive the incompressible Euler equation from the Vlasov-Poisson system by Brenier [3], to investigate hydrodynamic limits of the Boltzmann equation by Golse-Levermore-Saint-Raymond [12], Saint-Raymond [26] or to study gyrokinetic limits by Brenier [ 3 ] and Golse-Sa”