Analysis Seminar

: We consider the Kac particle system for the space-homogeneous Landau equation. For the Coulomb potential, we show that the Fisher information of the Liouville equation is monotonically decreasing in time. The monotonicity ensures the compactness to derive a weak solution of the Landau hierarchy. For hard potentials, we show that the propagation of exponential moments holds at the particle level. The moments bound ensures the uniqueness of weak solutions of the Landau hierarchy, which implies propagation of chaos.