Jacky Chong,Peking University

We consider the semiclassical limit from the Hartree equation with Coulomb interaction potential to the Vlasov–Poisson equation. Using a new stability estimate for the difference of the square roots of two solutions of the Vlasov–Poisson equation, we obtain the convergence in the L2 norm of the Wigner transform of a solution of the Hartree equation with Coulomb potential to a solution of the Vlasov–Poisson equation, with a rate of convergence proportional to ?. This improves on the result of ?3/4?ε rate of convergence in L2 obtained in [3]. If time permits, we shall discuss its connection to the derivation of Vlasov equation from many-body quantum dynamics given in [1]. The talk is based on our recent paper [2] with the same title. This is a joint work with Laurent Lafleche and Chiara Saffirio. The talk will be delivered in English.