Title: On Landau equation with harmonic potential: Nonlinear stability of time-periodic Maxwell Boltzmann distributions
Speaker: Chuqi Cao（The Hong Kong Polytechnic University）
Time: 8.5 (Tuesday), 10:00-11:00
Venue: Gewu Building 315
Abstract ：In this talk, we will provide the first and rigorous confirmations of the hypotheses by Ludwig Boltzmann within the context of the Landau equation in the presence of a harmonic potential. We will show that: (i) Each entropy-invariant solution can be identified as a time-periodic Maxwell-Boltzmann distribution. Moreover, these distributions can be characterized by thirteen conservation laws, which sheds light on the global dynamics. (ii) Each time-periodic Maxwell-Boltzmann distribution is nonlinearly stable. Furthermore, the convergence rate is entirely reliant on the thirteen conservation laws and is optimal when compared to the linear scenario. This talk is based on a joint work with Ling-Bing He and Jie Ji.
