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On Kac's chaos and related problems
This paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac \cite{Kac1956} in his study of mean-field limit for systems ofExpand
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The derivation of swarming models: Mean-field limit and Wasserstein distances
These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived asExpand
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WASSERSTEIN DISTANCES FOR VORTICES APPROXIMATION OF EULER-TYPE EQUATIONS
We establish the convergence of a vortex system towards equations similar to the 2D Euler equation in vorticity formulation. The only but important difference is that we use singular kernel of theExpand
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Particles approximations of Vlasov equations with singular forces : Propagation of chaos
We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geqExpand
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Propagation of chaos for the Landau equation with moderately soft potentials
We consider the 3D Landau equation for moderately soft potentials ($\gamma\in(-2,0)$ with the usual notation) as well as a stochastic system of $N$ particles approximating it. We first establish someExpand
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N-particles Approximation of the Vlasov Equations with Singular Potential
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 $$\alpha \leqq 1$$.Expand
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Propagation of chaos for the 2D viscous vortex model
We consider a stochastic system of $N$ particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution ofExpand
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Stability Issues in the Quasineutral Limit of the One-Dimensional Vlasov–Poisson Equation
This work is concerned with the quasineutral limit of the one-dimensional Vlasov–Poisson equation, for initial data close to stationary homogeneous profiles. Our objective is threefold: first, weExpand
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On two-dimensional hamiltonian transport equations with Llocp coefficients
Abstract We consider two-dimensional autonomous divergence free vector-fields in L loc 2 . Under a condition on direction of the flow and on the set of critical points, we prove the existence andExpand
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Mean field limit for the one dimensional Vlasov-Poisson equation
  • M. Hauray
  • Mathematics, Physics
  • 10 September 2013
We consider systems of $N$ particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, weExpand
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