N-particles Approximation of the Vlasov Equations with Singular Potential

By M. Hauray, Pierre-Emmanuel Jabin. 2003

156 citations recorded by the source corpus.

AbstractWe prove the convergence in any time interval of a point-particle approximation of the Vlasov equation by particles initially equally separated for a force in 1/|x|α, with $$\alpha \leqq 1$$. We introduce discrete versions of the L∞ norm and time averages of the force-field. The core of the proof is to show that these quantities are bounded and that consequently the minimal distance between particles in the phase space is bounded from below.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/2fb109365ddd91fbbecea943af3793fdc329aa28

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

A well-posedness theory in measures for some kinetic models of collective motion (2009, background): “This is a well-known limitation in the literature for working with the mean field limit and measure solutions, see [32, 21] and the references therein.”
Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces (2015, background): “The only results for deterministic second order systems with singular (non-Lipschitz) kernels without truncation are [27] and the more recent [28] for the propagation of chaos.”
A review of the mean field limits for Vlasov equations (2014, background): “3) for singular kernels F without truncation are [86, 87].”
On Kac's chaos and related problems (2012, background): “5) is also well adapted for proving quantitative propagation of chaos for deterministic dynamics associated to the Vlasov equation with regular interaction force [25] as well as singular interaction force [35, 34].”
Particles approximations of Vlasov equations with singular forces : Propagation of chaos (2011, methodology): “There is here a major improvement with respect to [34].”
From Newton to Boltzmann: Hard Spheres and Short-range Potentials (2012, result): “We refer to [11, 41] for pioneering results, to [25] for a recent study and to [21] for a review on that topic.”
Thermodynamics and dynamics of systems with long-range interactions (2010, background): “[54], and a more recent work, [58], for some classes of singular potential).”
On Landau damping (2009, background): “(12) In a related subject, this singularity is also the reason why the Vlasov–Poisson equation is still far from being established as a mean-field limit of particle dynamics (see [37] for partial results covering much less singular interactions).”