Jacob Bedrossian and Nader Masmoudi were awarded the 2019 SIAM Activity Group on Analysis of Partial Differential Equations Prize (SIAG/APDE Prize) for their paper, “Inviscid Damping and the Asymptotic Stability of Planar Shear Flows in the 2D Euler Equations,” Publications Mathématiques de l’IHÉS in 2015. The prize was awarded at the 2019 SIAM Conference on Analysis of Partial Differential Equations (PD19), held December 11-14 in La Quinta, California. Bedrossian accepted the award and presented the paper in a talk of the same title on December 13, 2019.
The SIAM Acitivity Group on Analysis of Partial Differential Equations awards the SIAG/APDE Prize every two years to the authors of the most outstanding paper, according to the prize committee, on a topic in PDE published in a peer-reviewed journal in the four calendar years preceding the award year. The 2019 prize committee states that Bedrossian and Masmoudi’s work opens a broad new avenue of research, pioneering the rigorous approach to inviscid damping as a mechanism for stability in ideal fluid flows.
Jacob Bedrossian is a Professor of Mathematics at the University of Maryland, College Park. He received his Ph.D. in 2011 at the University of California, Los Angeles and was then an NSF postdoctoral fellow (2011-2014) at the Courant Institute of Mathematical Sciences, New York University. His recent research is focused on partial differential equations arising mainly in fluid mechanics and plasma physics, and he is currently interested in understanding stability, coherent structure, mixing, and turbulence.
Nader Masmoudi has been a Professor at the Courant Institute of Mathematical Sciences, New York University, since 2000. He received degrees in mathematics from the École Normale Supérieure Paris in 1996, his Ph.D. from Paris Dauphine University in 1999, and his HDR in 2000. He was a CNRS researcher from 1998 to 2000. Masmoudi was a recipient of the Fermat Prize in 2017. He is currently spending a few years at New York University Abu Dhabi (NYUAD) as an affiliated faculty.
Q: Why are you excited to be awarded the SIAG/APDE Prize?
A: It is a great honor to be awarded this prize, especially given how many exciting papers are being produced in the field of PDE right now and in recent years. We hope that this prize helps to encourage more researchers to become interested in the fascinating field of hydrodynamic stability and the widening variety of interesting work being pursued there now.
Q: Could you tell us a bit about the research that won you the prize?
A: Over-simplifying a little, there are two basic types of flows that fluids, such as air or water, can take: laminar or turbulent. Laminar flow means the flow is in organized layers; examples are shear flows, in which the fluid is moving in straight lines, or a vortex, in which the fluid is flowing in circles or spirals. The other state is turbulent, in which the fluid is chaotic and characterized by the formation and dissipation of eddies of many different length-scales. One reason for a fluid to remain laminar is if internal friction (the viscosity) is dominant, such as in a jar of honey. However, in many settings the viscosity is weak and does not explain why certain flows remain laminar while other flows become unstable and transition into turbulent flows.
Our work provides the first mathematical proof that a different mechanism, called inviscid damping, can play a crucial role in understanding stability in fluids when the viscosity is negligible. This stabilizing effect is due to the differential rotation or shear in a fluid, and so can explain why some laminar flows are more stable than others. In a mathematically idealized setting, we showed that this mechanism can make shear flows asymptotically stable (in a sense) for the nonlinear two-dimensional fluid equations even with no viscosity at all. In this case, the equations are actually time-reversible, so this stability mechanism is quite different from that traditionally studied in fluid mechanics. It is more like a type of dispersion, and is related to a phenomenon known as Landau damping in plasma physics. This connection with Landau damping was important for us, as the work of Clément Mouhot and Cedric Villani was very inspirational to us as we started to understand inviscid damping. Our first work provided a base point in which to expand on the mathematical and physical ideas in fluid mechanics, both for our collaborators and us, and also for several other groups of researchers who have now started to investigate in new and exciting related directions.
Q: What does your research mean to the public?
A: How, when, and why laminar flow transitions to turbulent flow and the motion of coherent structures are important aspects of many practical fluid applications, such as in vehicle design and weather modeling. While the initial works in the mathematics community have been in idealized settings which seem far removed from such applications, we are hoping that in the long-term, our research will help lay the groundwork for a deeper theoretical understanding of coherent structure and laminar-to-turbulent transition in fluid mechanics.
Q: What does being a SIAM member mean to you?
A: The scientific diversity represented in SIAM is crucial for strengthening and maintaining the links between the many different branches of applied mathematics and also the links between those closer to applications, such as engineers and physicists, with more theory-oriented mathematicians, such as those working in applied analysis of PDE.