On the L2 Rate of Convergence in the Limit from the Hartree to the Vlasov–Poisson Equation
Time: 2022-10-31
Published By: He Liu
Speaker(s): Jacky Chong (PKU)
Time: 16:20-17:20 November 3, 2022
Venue: Room 77201, Jingchunyuan 78, BICMR
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 h. This improves the result of h^{3/4−ε} rate of convergence in L2 obtained previously. Based on a joint work with Laurent Lafleche and Chiara Saffirio.
