Seminar| Institute of Mathematical Sciences
Time: Thursday, January 8th, 2026,13:30-14:30
Location: IMS, RS408
Speaker: Zhuo Xu, University of Bordeaux
Abstract: In this talk, we present a stabilization result for a simplified one-dimensional fluid-particle interaction system. First, without any smallness assumptions, we establish a non-collision property: the particle never reaches the fluid boundary in finite time, which in turn yields global well-posedness of the interaction system. Next, we study a stabilization problem for this model. In the absence of feedback control, the particle converges to an a priori unknown limit position that cannot be described solely by the initial data. To regulate the final position of the particle to an arbitrary target, we employ a proportional feedback control acting on the particle and prove that both the position error and the total kinetic energy of the closed-loop system decay exponentially to zero.