Recent Progress in Searching for Finite Time Singularities of 3D Euler Equations and Related Models
Abstract
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. A potential singularity in the 3D Euler equations is significant because it may be responsible for the onset of energy cascade in turbulent flows. The speaker and his research group first review some recent theoretical and computational studies of the 3D Euler equations. Their study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. Recent computations have provided strong numerical evidence that the 3D Euler equations develop a finite time singularity from smooth initial data. The speaker will report some recent progress in providing a rigorous justification of the singularity formation in the 3D Euler equations and related models.
About the speaker
Prof. Thomas Hou received his Bachelor Degree from South China University of Technology in 1982, and his PhD from UCLA in 1987. Upon graduating from UCLA, he researched at the NYU Courant Institute and then became a faculty member in 1989. He moved to the Applied Math Department at Caltech in 1993, and is currently the Charles Lee Powell Professor of Applied and Computational Mathematics at Caltech.
Prof. Hou is one of the leading experts in vortex dynamics and multiscale problems. His research interests are centered around developing analytical tools and effective numerical methods for vortex dynamics, interfacial flows, and multiscale problems. In recent years, he has devoted considerable effort to investigate the 3D Euler singularity and the Clay Millennium Problem on the Navier-Stokes equations. He was also the founding Editor-in-Chief of the SIAM Journal on Multiscale Modeling and Simulation (2002-2007) and the founding Co-Editor-in-Chief of the Advances in Adaptive Data Analysis (2009-2015).
Prof. Hou has received a number of honors and awards, including Fellow of the American Mathematical Society (2012), Fellow of the American Academy of Arts and Sciences (2011), the SIAM Fellow (2009), the Computational and Applied Sciences Award from USACM (2005), the Morningside Gold Medal in Applied Mathematics (2004), the SIAM Wilkinson Prize in Numerical Analysis and Scientific Computing (2001), the Francois N Frenkiel Award from the Division of Fluid Mechanics of APS (1998), the Feng Kang Prize in Scientific Computing (1997), the Sloan Fellowship (1990-1992).
