Guo Luo and Thomas Y. Hou were awarded the SIAM Outstanding Paper Prize at the 2018 SIAM Annual Meeting. They were recognized for their paper, “Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation,” Multiscale Modeling and Simulation, Volume 12, Issue, 4 (2014).
The SIAM Outstanding Paper Prize is awarded to the authors of the three most outstanding papers published in SIAM journals. Priority is given to papers that bring a fresh look at an existing field or that open up new areas of applied mathematics.
Guo Luo received his BSc in applied mathematics from Zhongshan (Sun Yat-sen) University in 2001, his MPhil in computer science from the Chinese University of Hong Kong in 2003, and his PhD in mathematics from the Ohio State University in 2009. Before joining the City University of Hong Kong in 2014, he worked as a von Karman Postdoctoral Instructor at California Institute of Technology. His research interests include formation of finite-time singularities in 3D Navier-Stokes/Euler equations and other related problems, efficient numerical solution of singular or nearly singular partial differential equations, mesh adaptation strategies, computational fluid dynamics, and scientific computing.
Thomas Yizhao Hou is the Charles Lee Powell Professor of Applied and Computational Mathematics at California Institute of Technology. He received his PhD from UCLA in 1987 and joined the Courant Institute, New York University. He 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 as a tenured associate professor and was named the Charles Lee Powell Professor in 2004. Hou received SIAM’s James H. Wilkinson Prize in Numerical Analysis and Scientific Computing in 2001 and was elected a member of the inaugural class of SIAM Fellows in 2009. He was also the founding Editor-in-Chief of Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, serving as Editor-in-Chief from 2002 to 2007. His research interests include 3D Euler singularity, interfacial flows, multiscale problems, and adaptive data analysis.
Below are Thomas Y. Hou’s answers about receiving the SIAM Outstanding Paper Prize.
Q: Why are you excited to receive this prize?
A: I am very honored to receive the 2018 SIAM Outstanding Paper Prize for my joint paper with Dr. Guo Luo. My collaborators and I have been working on the 3D Euler singularity for more than a decade. It is really exciting that we have found a class of initial boundary conditions that could potentially lead to finite time singularity for the 3D Euler equations. This work has generated a lot of interest in the mathematics and the fluid dynamics community and inspired a number of subsequent developments.
Q: Could you tell us a bit about the research that won you the prize?
A: The 3D Euler singularity is extremely challenging and is closely related to the Clay Millennium Problem on the 3D Navier-Stokes equations. Due to the nonlocal nature of the nonlinearity and some subtle dynamic depletion of vortex stretching, it is very difficult to nail down a 3D Euler singularity. Our paper has provided convincing numerical evidence that the 3D Euler equations develop a finite time singularity. One of the key ideas is to impose a lot of symmetry on the solution to obtain a stable and sustainable blow-up mechanism.
Q: What does your research mean to the public?
A: Physicists and engineers have used the Navier-Stokes equations to model ocean currents, weather patterns, and the turbulent air currents that follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the ocean currents and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. One of the main open questions is whether the Navier-Stokes equations could develop some singular behavior (like a perfect storm) if we start with a perfectly smooth initial profile with finite energy. My joint work with Dr. Guo Luo shows that the 3D Euler equations, which can be considered as particular Navier-Stokes equations with zero viscosity, can develop some singular behavior from a smooth initial profile if certain symmetry is imposed on the flow.
Q: What does being a SIAM member mean to you?
A: Being a SIAM member has meant a lot to me. SIAM has played an important role in my professional development and also provides an opportunity for me to serve the applied mathematics community. From 1992 to 1997, I served on the editorial board of SIAM Journal on Numerical Analysis. In 2002, I worked with a group of leading experts to found the SIAM interdisciplinary journal Multiscale Modeling and Simulation, which has been a great success. I was also fortunate to have the opportunity to serve on the SIAM Council for two terms from 2009 to 2014.
Learn more about the SIAM Outstanding Paper Prizes.