Journal of Mathematical Fluid Mechanics - Birkhäuser Distinguished Lectures in Mathematical Fluid Mechanics
The Journal of Mathematical Fluid Mechanics (JMFM) is proud to showcase the 2023 Birkhäuser Distinguished Lecture (this opens in a new tab) sponsored and organised by Birkhäuser on behalf of the Editorial Board of JMFM. The Birkhäuser Distinguished Lecture is very much in line with the scope of JMFM and lecturers are selected by the Editorial Board.
Lecturer: Professor Thomas Yizhao Hou
Professor Thomas Yizhao Hou is a world-class applied and computational mathematician. He received his BSc and PhD degrees in mathematics from South China University of Technology and University of California, Los Angeles in 1982 and 1987, respectively. After obtaining his PhD, he worked as a postdoc, an assistant and an associate professors in Courant Institute from 1987 to 1993. He joined the faculty of California Institute of Technology in 1993 and became Charles Lee Powell Professor of Applied and Computational Mathematics in 2004.
Professor Hou has made groundbreaking contributions to several frontier areas in applied mathematics, including computational fluid dynamics, multiscale analysis, and singularity formation of three-dimensional incompressible Euler and Navier-Stokes equations. Prof. Hou has received a number of awards and honors, including Alfred P. Sloan Research Fellowship in 1990, Feng Kang Prize in Scientific Computing in 1997, Francois Frenkiel Award from American Physical Society in 1998, James H. Wilkinson Prize in Numerical Analysis and Scientific Computing from SIAM in 2001, Morningside Gold Medal in Applied Mathematics in 2004, the Computational and Applied Sciences Award from United States Association of Computational Mechanics in 2005, SIAM Outstanding Paper Prize in 2018, and the SIAM Ralph E. Kleinman Prize in 2023. Prof. Hou was also an invited Speaker at International Congress of Mathematicians in 1998 and a plenary speaker at International Congress on Industrial and Applied Math in 2003. Prof. Hou was elected SIAM Fellow in 2009, Fellow of American Academy of Art and Sciences in 2011, and Fellow of American Mathematical Society in 2012. He has served as the founding Editor-in-Chief of SIAM first interdisciplinary journal “Multiscale Modeling and Simulation” from 2002 to 2007.
Date: 1st December, 2023
Time: 8:00 - 9:00 AM (Pasadena, California, USA) / 11:00 -12:00 (New York) /16:00-17:00 (London)
Title: Potentially singular behavior of 3D incompressible Navier-Stokes equations
Abstract: Whether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, I will present some new numerical evidence that the 3D Navier-Stokes equations develop nearly self-similar singular scaling properties with maximum vorticity increased by a factor of 107107. This potentially singular behavior is induced by a potential finite time singularity of the 3D Euler equations. Unlike the Hou-Luo blowup scenario, the potential singularity of the 3D Euler and Navier-Stokes equations occurs at the origin. We have applied several blowup criteria to study the potentially singular behavior of the Navier-Stokes equations. The Beale-Kato-Majda blow-up criterion, the blowup criteria based on the growth of enstrophy and negative pressure, the Ladyzhenskaya-Prodi-Serrin regularity criteria all seem to imply that the Navier-Stokes equations develop nearly singular behavior. Finally, we present some new numerical evidence that a class of generalized axisymmetric Navier-Stokes equations with time dependent fractional dimension and nonlinear rotation force seem to develop asymptotically self-similar blowup.
The lecture was hosted via Zoom (this opens in a new tab) by Dr Pin Wu (publishing editor) and Professor Giovanni P. Galdi (editor-in-chief) and was free to attend. It included a presentation and a brief Q+A session.
The recording of the lecture is available on the Birkhäuser Distinguished Lectures (this opens in a new tab) channel, where you may also find past lectures.