走向现代数学学术报告 - 李子劲副教授（No. 884)

报告题目：On the uniqueness of stationary NS in an infinite-long pipe with the Navier-slip boundary

报告时间：2025年12月1日 10:30

报告地点：东海岸校区-D实209

报 告 人：李子劲 副教授（南京信息工程大学）

邀 请 人：吴忠二 博士

报告摘要：In this talk, we consider the stationary Navier-Stokes equations with the Navier-slip boundary condition in an infinite pipe $\mD=\Sigma\times\mR$. We show that if the flux $\Phi$ of the solution is no larger than a critical value independent of the friction ratio of the Navier-slip boundary condition, the solution to the problem must be the parallel Poiseuille flow with the given flux. Compared with known related 3D results, this seems to be the first conclusion with the size of critical flux being uniform with the friction ratio $\al\in]0,\infty]$, and it is surprising since the prescribed uniqueness breaks down when $\alpha=0$, even if $\Phi=0$. Our proof relies primarily on a refined gradient estimate of the Poiseuille flow with the Navier-slip boundary condition. Additionally, we prove the critical flux $\Phi_0\geq\f{\pi}{16}$ provided that $\Sigma$ is a unit disk. This is a joint work with Ning Liu and Taoran Zhou. Additionally, some related works (with Xinghong Pan and Jiaqi Yang) on generalized Leray's problem with the Navier-slip boundary condition are also included.

报告人简介：李子劲，南京信息工程大学数学与统计学院副教授，硕士生导师。2012年本科毕业于南京大学数学系，2019年博士毕业于南京大学数学系，期间在美国加州大学公派联合培养2年。长期从事流体力学偏微分方程研究，在J. Funct. Anal.、J. Math. Pures Appl.、Sci. China Math.、 J. Differ. Equations、Calc. Var. PDE、Commun. Contemp. Math.等期刊发表论文二十余篇。多次主持国家级、省部级科研项目。