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DESCRIPTION:Speaker: Thomas Hou, Caltech
Talk Title: Recent progress on singularity formation of 3D incompressible Euler and Navier-Stokes equations
Abstract: Abstract: Whether the 3D incompressible Euler and Navier equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in fluid dynamics. In this talk, I will present a recent result with Dr. Jiajie Chen in which we prove finite time blowup of the 2D Boussinesq and 3D Euler equations with smooth initial data. There are several essential difficulties in establishing such blowup result. We overcome these difficulties by decomposing the solution operator into a leading order operator that enjoys sharp stability estimates plus a finite rank perturbation operator that can be estimated by using computer assisted proof. This enables us to establish nonlinear stability of the approximate self-similar profile and prove nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations. I will also report some recent progress on potentially singular behavior of the 3D incompressible Navier-Stokes equations.
Biography: Thomas Yizhao 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 Ph.D. from UCLA in 1987, and became a tenure track assistant professor at the Courant Institute in 1989, and a tenured associate professor in 1992. He moved to Caltech in 1993 and was named the Charles Lee Powell Professor in 2004. Dr. Hou has received a number of honors and awards, including 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 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 also the founding Editor-in-Chief of the SIAM Journal on Multiscale Modeling and Simulation from 2002 to 2007.
Host: AME Department
More Info: https://ame.usc.edu/seminars/
Webcast: https://usc.zoom.us/j/95805178776?pwd=aEtTRnQ2MmJ6UWE4dk9UMG9GdENLQT09
SEQUENCE:5
DTSTART:20230329T153000
LOCATION:SLH
DTSTAMP:20230329T153000
SUMMARY:AME Seminar
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DTEND:20230329T163000
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