Recent Progress on Potential Singularity of the 3D Navier-Stokes Equation and Related Models by Prof Thomas Hou (Caltech)

About the talk

Whether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the seven Clay Millennium Prize Problems. We first review our recent work in developing a rigorous computer assisted proof of the 3D Euler singularity with smooth initial data and boundary. We then present some numerical evidence that the 3D Navier-Stokes equations develop a tornado type of traveling wave singularity at the origin. This potentially singular behavior is induced by a potential finite time singularity of the 3D Euler equations. We have applied several blowup criteria to confirm this potentially singular behavior of the Navier-Stokes equations. 

Our Distinguished Speaker

Prof Thomas Hou is the Charles Lee Powell professor of applied and computational mathematics at Caltech. His research interests include 3D Euler singularity, interfacial flows, multiscale problems, and adaptive data analysis. He received his BS in math from South China University of Technology in 1982, his Ph.D. from UCLA in 1987,  became a tenure track assistant professor in 1989 and a tenured associate professor in 1992 at the Courant Institute. He moved to Caltech in 1993 and was named the Charles Lee Powell Professor in 2004.

Prof Hou has received a number of honors and awards, including Member of the National Academy of Sciences in 2024, Fellow of American Academy of Arts and Sciences in 2011, a member of the inaugural class of SIAM Fellows in 2009 and AMS Fellows in 2012, the William Benter Prize in Applied Mathematics in 2024, the SIAM Ralph E. Kleinman Prize in 2023, the SIAM Outstanding Paper Prize in 2018, the SIAM Review SIGEST Award in 2019, the Computational and Applied Sciences Award from USACM in 2005, the Morningside Gold Medal in Applied Mathematics in 2004, the SIAM Wilkinson Prize in Numerical Analysis and Scientific Computing in 2001, the Frenkiel Award from the Division of Fluid Mechanics of American Physical Society in 1998, the Feng Kang Prize in Scientific Computing in 1997, a Sloan fellow from 1990 to 1992. He was an invited speaker at the International Congress of Mathematicians in 1998, an invited plenary speaker at the International Congress of Industrial and Applied Mathematics in 2003, and the founding Editor-in-Chief of the SIAM Journal on Multiscale Modeling and Simulation from 2002 to 2007.

Co-organisers:

• Institute of Advanced Studies (IAS)
• School of Physical and Mathematical Sciences (SPMS)
• Graduate Students’ Club of SPMS