学术报告（刘双乾 2025.12.29）

Abstract:  In this talk, I will report on our recent work on a free boundary value problem for the Boltzmann equation, where the boundary motion is governed by an ordinary differential system derived from Hooke's law and is coupled with the drag force exerted by the surrounding particles. A central difficulty of this problem lies in the strong interaction between the kinetic dynamics and the free boundary. To address this issue, we introduce a novel conformal transformation that reduces the moving-domain problem to a fixed reference domain. A key observation is that the kinetic distribution and the free boundary variables, when considered jointly, generate a natural quadratic energy structure that reveals intrinsic damping and cancellation effects at the boundary. Exploiting this structure, we establish global-in-time existence of solutions via an $L^\infty-L^2$ framework. Furthermore, the uniqueness of solutions is obtained by proving localized weighted $W^{1,p}$ estimate, which yield stability in $L^{1+}$.