学术报告：Navier-Stokes方程解的存在性和光滑性

报告人：窦华书， 浙江理工大学教授、博导。
& t* y; h1 x: _2 @5 A预订报告日期：2023年4月26日（星期三），北京时间晚上9:00开始。
$ }; o( q* H. H( X2 _Wednesday, April 26, 2023 Time: 9am EST (3pm Central European； 9pm Beijing)
! u& f) e% c8 a, p* H0 GZoom Link: Meeting ID: 985 8096 1819, Passcode: 2099
Title: Existence and Smoothness of Solution of the Navier-Stokes Equation
4 l: A  t7 B/ I9 E1 |Presenter: Prof. Hua-Shu Dou (School of Mechanical Engineering, Zhejiang Sci-Tech University, China)
Abstract
9 v) o7 q% q) k* i* [( I: f# ^Existence and smoothness of solution of the Navier-Stokes equation are exactly disproved for the first time by using two different approaches: Energy gradient theory and Poisson equation method. At a higher Reynolds number, the velocity profile in laminar flow is distorted under a disturbance and velocity deficit is produced. It is found that the viscous term is zero instantaneously, leading to the mechanical energy gradient to be zero , and velocity discontinuity occurs at a distorted position, which forms the singularity of Navier-Stokes equation. In addition, the singularity of the Navier-Stokes equation at the zero source term location is also confirmed by the analysis of the Poisson equation. The analytical results show that the singularity of the Navier-Stokes equation is the cause of turbulent transition and the inherent mechanism of sustenance of fully developed turbulence, which is in agreement with experiments and simulations. Since the velocity is not differentiable at the singularity, there exist no smooth and physically reasonable solutions of Navier-Stokes equations at high Reynolds number (beyond laminar flow).
Bio of the speaker
Dr. Hua-Shu Dou received his Ph.D from Beijing University of Aeronautics and Astronautics in 1991. Then, he worked at Tsinghua University, The University of Sydney, and National University of Singapore from 1991 to 2011. Since 2011, he is a Chair Professor at Zhejiang Sci-Tech University. His researches focused on flow instability and turbulent transition, computational fluid dynamics, combustion and detonation, turbomachinery, non-Newtonian flow and multiphase flows, etc. He holds more than 160 published papers and two books (one is co-authored) published by Springer. He is an AIAA associate fellow and Member of APS and ASME.
报告题目：Navier-Stokes方程解的存在性和光滑性
报告人：窦华书, 浙江理工大学，杭州
摘要：通过两种不同的理论方法：能量梯度理论和泊松方程方法，首次精确地证否了Navier-Stokes方程的解的存在性和光滑性。在雷诺数较高的情况下，层流中的速度分布在扰动下发生畸变，产生速度亏损。研究发现，在速度畸变的位置，粘性项瞬时为零，引起此处机械能梯度为零，速度间断发生，这导致了Navier-Stokes方程的奇异性。此外，利用泊松方程的分析方法也证实了Navier-Stokes方程在零源项的位置的奇异性。分析结果表明，Navier-Stokes方程的奇异性是湍流转捩和湍流产生的原因，也是完全发展的湍流得以维持的内在机制，这与实验测量和数值模拟结果惊人的一致。由于速度在奇点处是不可微分的，因此在高雷诺数下（对转捩流动和湍流流动），Navier-Stokes方程不存在光滑且物理上合理的解。
这项研究结果，精确地回答了千禧年大奖难题之一： 纳维-斯托克斯方程的解的存在性和光滑性。即： 纳维-斯托克斯方程不存在全局域上的光滑解。
( J  |- M/ w9 ]6 |( O: w报告人简介
5 i/ O2 \3 G( n# V3 F窦华书教授，分别于1982和1984年在东北大学获得学士和硕士学位，于1991年在北京航空航天大学获得空气动力学专业博士学位。然后，1991年至2011年在清华大学、悉尼大学和新加坡国立大学工作，整整20年。期间有2年时间访问日本东北大学和日本法政大学。2011年起，作为海外高层次人才引进到浙江理工大学全职工作、任特聘教授。研究领域是流动稳定性和湍流、计算流体动力学、燃烧和爆轰、热力叶轮机械、非牛顿流动和多相流等。他持有160多篇已发表的论文和Springer出版的两本专著（其中一本是合著的）。他是美国航空航天学会AIAA Associate Fellow, Member of APS（美国物理学会） and ASME（美国机械工程师协会）。
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