主题：Liouville-Type theorems for steady solutions to the Navier-Stokes system in a slab板内纳维-斯托克斯系统稳定解的刘维尔型定理

主讲人：澳门大学 桂长峰教授

主持人：数学学院 陈新富教授

时间：2025年4月29日（周二）9:30-10:20

地点：柳林校区通博楼B412会议室

主办单位：数学学院 科研处

主讲人简介：

桂长峰，澳门大学数学系讲座教授，数学系主任，澳大发展基金会数学杰出学者，博士生导师。1991年在美国明尼苏达大学获博士学位。桂长峰教授曾入选国家级人才计划和海外高层次人才，入选美国数学会首届会士，美国西蒙斯会士、美国科学促进会会士，曾获得过IEEE最佳论文奖、加拿大太平洋数学研究所研究成果奖、加拿大数学中心Andrew Aisensdadt 奖等荣誉。桂长峰教授研究方向为非线性偏微分方程、图像分析和处理，特别是在Allen-Cahn方程的研究、Moser-Trudinger不等式最佳常数的猜想、De Giorgi 猜想和Gibbons 猜想等方面取得了一系列在国际上有重大影响的工作，在国际顶一流数学期刊上发表80余篇，其中包括《Annals of Mathematics》《Inventiones Mathematicae》《Communications on Pure and Applied Mathematics》等顶级期刊。

内容提要：

In this talk, I will present recent results on Liouville-type theorems for the steady incompressible Navier-Stokes system in a three-dimensional slab with either no-slip boundary conditions or periodic boundary conditions. When the no-slip boundary conditions are prescribed, we prove that any bounded solution is trivial if it is axisymmetric or rur is bounded, and that general three-dimensional solutions must be Poiseuille flows when the velocity is not big. When the periodic boundary conditions are imposed on the slab boundaries, we prove that the bounded solutions must be constant vectors if either the swirl velocity is independent of the angular variable, or rur decays to zero as r tends to infinity, The proofs are based on the fundamental structure of the equations and energy estimates. The key technique is to establish a Saint-Venant type estimate that haracterizes the growth of Dirichlet integral of nontrivial solutions. The talk is based on a recent joint work with Jeaheang Bang, Yun Wang and Chunjing Xie.