Well-posedness of the spatially homogeneous Landau equation for soft potentials

Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules

We prove a quantitative propagation of chaos, uniformly in time, for the spatially homogeneous Landau equation in the case of Maxwellian molecules. We improve the results of Fontbona, Guérin and Méléard \cite{FonGueMe} and Fournier \cite{Fournier} where the propagation of chaos is proved for finite time. Moreover, we prove a quantitative estimate on the rate of convergence to equilibrium uniformly in the number of particles.

The Landau Equation for Maxwellian molecules and the Brownian Motion on SO_R(N)

In this paper we prove that the spatially homogeneous Landau equation for Maxwellian molecules can be represented through the product of two elementary processes. The first one is the Brownian motion on the group of rotations. The second one is, conditionally on the first one, a Gaussian process. Using this representation, we establish sharp multi-scale upper and lower bounds for the transition density of the Landau equation, the multi-scale structure depending on the shape of the support of the initial condition.

麦克斯韦分子朗道方程粒子近似的相对熵方法

Relative Entropy Method for Particle Approximation of the Landau Equation for Maxwellian Molecules

本文通过相对熵方法，从随机相互作用粒子系统推导出麦克斯韦分子的空间均匀朗道方程，建立了密度函数对数梯度与黑塞估计及新的大数定律结果。

朗道方程的Kac近似的时间一致相对熵估计

Uniform-in-time relative entropy estimates for Kac's approximation of the Landau equation

该研究针对三维麦克斯韦分子朗道方程的Kac粒子近似，证明时间一致的定量相对熵估计，得到$N^{-1/2}$阶有限时间归一化熵界，推导混沌的时间一致传播。

Propagation of chaos for the Landau equation with moderately soft potentials

We consider the 3D Landau equation for moderately soft potentials ($γ\in(-2,0)$ with the usual notation) as well as a stochastic system of $N$ particles approximating it. We first establish some strong/weak stability estimates for the Landau equation, which are satisfying only when $γ\in [-1,0)$. We next prove, under some appropriate conditions on the initial data, the so-called propagation of molecular chaos, i.e. that the empirical measure of the particle system converges to the unique solution of the Landau equation. The main difficulty is the presence of a singularity in the equation. When…

Asymptotic of grazing collisions for the spatially homogeneous Boltzmann equation for soft and Coulomb potentials

We give an explicit bound for the Wasserstein distance with quadratic cost between the solutions of Boltzmann's and Landau's equations in the case of soft and Coulomb potentials. This gives an explicit rate of convergence for the grazing collisions limit. Our result is local in time for very soft and Coulomb potentials and global in time for moderately soft potentials.