Speaker：Tao Zhou (University of Macau)

Time：2026-7-24 10:30

Location：Conference Room C610 at Administration Building at Haiyun Campus

Abstract:

In this talk, we study the global existence of weak solutions for the Cucker-Smale-Navier-Stokes system in an infinitely long cylindrical domain with specular boundary condition. This system models the collective behavior of flocking particles in an incompressible viscous fluid, whereas the specular boundary condition allows particles to collide with the cylinder wall elastically.

This generalize the previous results for Stokes type equations, and is the first result to study the flocking particles interacting with Navier-Stokes flows in an infinitely long channel. This involves substantial analytical challenges, especially the treatments of nonlinear convection term. In this work, we overcome these difficulties by employing Ladyzhenskaya's inequality and Gronwall's lemma. Moreover, we establish the flocking estimates and demonstrate convergence toward flocking states asymptotically.