Particle approximations of Landau equation with moderately soft potentials
We will discuss a (non-conservative) "particle" system approximating the homogeneous 3D Landau equation.
In that system, the drift and diffusion coefficients of each particle, depends on the other ones in a "mean-field" way.
We are interested by the so called "propagation of molecular chaos", in other words the limit towards Landau when the number of particles goes to infinity. In the case of moderately soft potentials, the interaction is singular, and the usual theory do not apply.
Here, we will present two methods to prove the propagation of chaos:
the first one is qualitative and apply to quite soft potential ($\gamma \in (-2,0)$),
the second one is quantitative, but apply to not to soft potential ($\gamma \in (-1,0)$).