报告人：周韬（澳门大学）

时 间：2026年7月24日10:30

地 点：海韵园行政楼C610

内容摘要:

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.

个人简介：

周韬，2018年毕业于英国曼彻斯特大学获金融数学荣誉学士学位，2022年毕业于韩国首尔国立大学获基础数学硕士学位，2025年毕业于香港中文大学获数学博士学位。曾先后在吉林大学和南京大学担任访问学者，现为澳门大学数学系博士后研究人员。主要研究方向为非线性偏微分方程，特别是流体力学、动理学理论中的偏微分方程理论。

联系人：王焰金