Seminar online: Existence and Smoothness of Solution of the Navier-Stokes Equation, April 26, 2023.

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 Speaker: 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 answered the Millennium Prize problem: the existence and smoothness of solution to the Navier-Stokes equation. That is, there is no smooth solution of the Navier-Stokes equation 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.

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