Well/ill-posedness bifurcation for the Boltzmann equation

開催日時
2023/04/21 金 16:00 - 17:00
講演者
Xuwen Chen
講演者所属
Department of Mathematics, University of Rochester
概要

We study the well/ill-posedness of the Boltzmann equation with dispersive methods. We take the constant collision kernel case as the 1st example. We construct a family of special solutions, which are neither near equilibrium nor self-similar, and prove the ill-posedness in $H^s$ Sobolev space for $s<1$, despite the fact that the equation is scale invariant at $s=1/2$. Combining with the previous work, we have found that exact well/ill-posedness threshold.