We establish the well-posedness and some quantitative stability of the spatially homogeneous Landau equation for hard potentials, using some specific Monge-Kantorovich cost, assuming only that the initial condition is a probability measure with a finite moment of order p for some $p>2$. As a consequence, we extend previous regularity results and show that all non-degenerate measure-valued solutions to the Landau equation, with a finite initial energy, immediately admit analytic densities with finite entropy. Along the way, we prove that the Landau equation instantaneously creates Gaussian moments. We also show existence of weak solutions under the only assumption of finite initial energy.

我们建立适定性和空间均匀的Landau方程用于硬电位的一些定量稳定性，使用一些特定型Monge-的Kantorovich成本，假设仅在初始条件是与顺序的有限时刻一个概率测度p为一些$磷>2$. 因此，我们扩展了先前的正则性结果，并表明所有具有有限初始能量的 Landau 方程的非退化测度值解立即承认具有有限熵的解析密度。在此过程中，我们证明了朗道方程立即产生了高斯矩。我们还展示了在有限初始能量的唯一假设下弱解的存在。