報告人：竇華書，?浙江理工大學教授、博導。

預訂報告日期：2023年4月26日（星期三），北京時間晚上9:00開始。

Wednesday, April 26, 2023 Time: 9am EST (3pm Central European； 9pm Beijing)

Zoom Link: Meeting ID: 985 8096 1819, Passcode: 2099

Title: Existence and Smoothness of Solution of the Navier-Stokes Equation

Presenter:?Prof. Hua-Shu Dou?(School of Mechanical Engineering, Zhejiang Sci-Tech University, China)

Abstract

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).?This research result accurately answers one of the Millennium Prize problems: the existence and smoothness of solutions to the Navi Stokes equation. That is, for transitional flows and turbulence, the Navier-Stokes equation does not have smooth solutions in the global domain.

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.

報告題目：Navier-Stokes方程解的存在性和光滑性

報告人：竇華書, 浙江理工大學，杭州

摘要：通過兩種不同的理論方法：能量梯度理論和泊松方程方法，首次精確地證否了Navier-Stokes方程的解的存在性和光滑性。在雷諾數(shù)較高的情況下，層流中的速度分布在擾動下發(fā)生畸變，產(chǎn)生速度虧損。研究發(fā)現(xiàn)，在速度畸變的位置，粘性項瞬時為零，引起此處機械能梯度為零，速度間斷發(fā)生，這導致了Navier-Stokes方程的奇異性。此外，利用泊松方程的分析方法也證實了Navier-Stokes方程在零源項的位置的奇異性。分析結果表明，Navier-Stokes方程的奇異性是湍流轉捩和湍流產(chǎn)生的原因，也是完全發(fā)展的湍流得以維持的內(nèi)在機制，這與實驗測量和數(shù)值模擬結果驚人的一致。由于速度在奇點處是不可微分的，因此在高雷諾數(shù)下（對轉捩流動和湍流流動），Navier-Stokes方程不存在光滑且物理上合理的解。這項研究結果，精確地回答了千禧年大獎難題之一： 納維-斯托克斯方程的解的存在性和光滑性。即： 對轉捩流動和湍流，納維-斯托克斯方程不存在全局域上的光滑解。

報告人簡介

竇華書教授，分別于1982和1984年在東北大學獲得學士和碩士學位，于1991年在北京航空航天大學獲得空氣動力學專業(yè)博士學位。然后，1991年至2011年在清華大學、悉尼大學和新加坡國立大學工作，整整20年。期間有2年時間訪問日本東北大學和日本法政大學。2011年起，作為海外高層次人才引進到浙江理工大學全職工作、任特聘教授。研究領域是流動穩(wěn)定性和湍流、計算流體動力學、燃燒和爆轟、熱力葉輪機械、非牛頓流動和多相流等。他持有160多篇已發(fā)表的論文和Springer出版的兩本專著（其中一本是合著的）。他是美國航空航天學會AIAA Associate Fellow, Member of APS（美國物理學會） and ASME（美國機械工程師協(xié)會）。

This talk is one of the?Complex Fluids and Soft Matter (CFSM) Seminar Series, Website:?https://cecas.clemson.edu/zhenli/cfsm/

The picture in top is from Wu and Moin (2009).