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Publications Influence

On Kac's chaos and related problems

- M. Hauray, S. Mischler
- Mathematics
- 21 May 2012

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 of… Expand

84 12- PDF

The derivation of swarming models: Mean-field limit and Wasserstein distances

- J. Carrillo, Y. Choi, M. Hauray
- Mathematics
- 21 April 2013

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 as… Expand

142 8- PDF

WASSERSTEIN DISTANCES FOR VORTICES APPROXIMATION OF EULER-TYPE EQUATIONS

- M. Hauray
- Mathematics
- 1 August 2009

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 the… Expand

39 8

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 \geq… Expand

81 8- PDF

Propagation of chaos for the Landau equation with moderately soft potentials

- N. Fournier, M. Hauray
- Mathematics
- 8 January 2015

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 some… Expand

25 6- PDF

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

102 5- PDF

Propagation of chaos for the 2D viscous vortex model

- N. Fournier, M. Hauray, S. Mischler
- Mathematics
- 6 December 2012

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 of… Expand

73 5- PDF

Stability Issues in the Quasineutral Limit of the One-Dimensional Vlasov–Poisson Equation

- Daniel Han-Kwan, M. Hauray
- Mathematics, Physics
- 25 November 2013

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, we… Expand

25 4- PDF

On two-dimensional hamiltonian transport equations with Llocp coefficients

- M. Hauray
- Mathematics
- 1 July 2003

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 and… Expand

30 2- PDF

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, we… Expand

19 2- PDF

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