# NWCS22 Prize Spotlight

Congratulations to Roberto Camassa, the 2022 Martin Kruskal Lecturer, and Toan T. Nguyen, the 2022 T. Brooke Benjamin Prize recipient. Learn more about the prize recipients below.

## Roberto Camassa

Roberto Camassa, University of North Carolina at Chapel Hill, was selected to give the 2022 Martin Kruskal Lecture. He gave the lecture at the 2022 SIAM Conference on Nonlinear Waves and Coherent Structures (NWCS22) held in hybrid format in Bremen, Germany from August 30 – September 2, 2022.

The lecture, titled “Fluid-boundary Interaction: Confinement Effects, Stratification and Transport”, took place on Tuesday, August 30 at 5:30 p.m. Central European Summer Time.

The SIAM Activity Group on Nonlinear Waves and Coherent Structures awards the Martin Kruskal Lecture every two years to one individual for a notable body of mathematics and contributions in the field of nonlinear waves and coherent structures. The award may be given either for a single notable achievement or for a collection of such achievements.

Camassa is Kenan Distinguished Professor in the department of mathematics at the University of North Carolina (UNC) at Chapel Hill. He obtained his Ph.D. from the California Institute of Technology in 1990 with his primary adviser Ted Wu. He was a Director’s Postdoctoral Fellow at the Center for Nonlinear Studies (CNLS) of Los Alamos National Laboratory, where he continued on as Staff Member in the Theoretical Division, Mathematical Modeling and Analysis group, before moving to UNC.

Camassa's research interests include nonlinear evolution equations, mathematical modeling, and fluid mechanics. Together with Prof. Rich McLaughlin, Camassa has built a state-of-the-art fluids laboratory at UNC Chapel Hill, joint with the department of marine sciences, where numerous new phenomena in waves, turbulent mixing in stratified fluids, and air-liquid pumping in lung airway geometries have been discovered and explained mathematically.

**Q: Why are you excited to deliver the Martin Kruskal Lecture?**

**A**: The first time I met Martin Kruskal it was on a late afternoon at CNLS. I was there as a postdoc, studying models of water wave propagation. We were having a one-on-one discussion in front of the board in the CNLS conference room over something I was working on. It stretched well past dinner time, and well past my ability to answer his questions. His childlike curiosity and drive to dig deep into a subject, blocking everything else off, made him an instant role model for me. Receiving a prize named after him is an incredible honor and a humbling experience, but the real prize has been the privilege of having met him and worked on a board with him.

**Q: Could you tell us a bit about the research that won you the prize?**

**A**: My work is centered around mathematical modeling of wave propagation in fluids, and fluid mechanics at large. This is an area where many challenging, fundamental problems arise, and I have been fortunate enough to be able to develop models that can enhance, in a small part, our understanding of some of these phenomena. Being able to demonstrate the effectiveness of models with laboratory experiments has been one of the most rewarding experiences in my research, for which much of the credit has to be shared with collaborators and students in our Joint Fluids Lab at UNC.

**Q: What does your work mean to the public?**

**A**: Wave propagation is arguably the most common type of motion in nature, just think of how much in our life depends on light and sound. Its manifestation on the surface of bodies of water is probably the most familiar image that comes to mind when one thinks about waves. So, you have this intersection of two broad physical areas, waves and fluids, and it turns out that this place is the source of some of the most difficult, and some still unsolved, problems in mathematics and classical physics. Thus, you have strong challenges to mathematicians and physicists on the one hand, and on the other hand, concepts familiar to just about everybody. This has got to be a good area for research!

What I have done over the years, in collaboration with colleagues and students, has been centered at this intersection, and hopefully has contributed to enhance the understanding of a few phenomena in this area. For instance, investigations on the dynamics of density stratified fluids with turbulent jets led to predictions of how plumes of oil got trapped underwater in the Deep-Water Horizon Gulf oil spill of 2010. Studying the exchange of momentum between highly viscous fluids and moving objects in them, as well air flows over them, has led to predictions on how fluid parcels distribute and mix, and has shed light on how mucus is transported in lung airways. There are more examples of how fluids and waves are a fertile area of research with readily applicable results; it is all an extra bonus that these can be illustrated by very visual experiments, appreciable without the interface of sophisticated instruments. This allows us to organize demonstrations in our lab for visitors from all backgrounds and ages, and perhaps, helps attract bright young things to this fascinating research area.

**Q: What does being a member of SIAM mean to you?**

**A**: Mathematics plays a central role in just about every intellectual endeavor, and in turn SIAM plays a central role in fostering a host of important activities to nurture its growth, helping maintain its presence across disciplines and in the public at large. To be a member of this organization means being able to contribute to its goals, and to have access to a venue that connects the national and international community in the mathematical sciences.

## Toan T. Nguyen

Toan T. Nguyen, Pennsylvania State University, is the 2022 recipient of the T. Brooke Benjamin Prize, was awarded at the 2022 SIAM Conference on Nonlinear Waves and Coherent Structures (NWCS22).

The SIAM Activity Group on Nonlinear Waves and Coherent Structures awards the T. Brooke Benjamin Prize every two years to one mid-career established researcher for recent outstanding work on a topic in nonlinear waves, as evidenced by a body of work with at least one significant publication in English in a peer-reviewed journal within the four calendar years preceding the award year.

Nguyen received the prize in recognition of his extensive and deep contributions to the mathematical theory of the dynamics of gas and fluids. In particular, the award recognizes his original contributions to the understanding of the stability of shear flows and Prandtl layers. In the 2016 paper cited in the nominations for the prize, Nguyen introduced innovative and deep techniques to put on a rigorous footing the surprising phenomenon known as viscous destabilization, which had been observed experimentally but not understood mathematically. His contributions extend beyond this to a wide range of problems in the field and are fully deserving of the highest recognition.

Growing up, Nguyen was busy picking coffee beans in a small village in Dak Lak province, Vietnam, where it was more desired for kids to earn money at a coffee farm than commuting to a faraway village for school. He was the first kid in the village to finish middle and high school, before being sent off to Saigon for his undergraduate study in mathematics at Vietnam National University of Science.

He completed his Master's degree in 2006 under Dung Le at University of Texas at San Antonio and obtained his Ph.D. in 2009 at Indiana University under Kevin Zumbrun; after which, he held an Fondation Sciences Mathématiques de Paris postdoc research fellowship at the University of Pierre et Marie Curie, and a Prager assistant professorship at Brown University. He joined Pennsylvania State University in 2013, where he now is a professor of mathematics. He was awarded an AMS Centennial Fellowship in 2018 and a Simons Fellowship in Mathematics in 2019. His current research interests include hyperbolic and dispersive PDEs, fluid dynamics, kinetic theory, and general relativity.

**Q: Why are you excited to receive the T. Brooke Benjamin Prize?**

**A**: I am grateful for the selection to receive the T. Brooke Benjamin Prize and for the recognition of my research in fluid dynamics and plasma physics. I take the opportunity to thank my wife, Thanh Tran, and my son Alex for their love and support throughout the years. Most of my work is accomplished through collaborative efforts, and the research that is being recognized is no exception. I would like to acknowledge the support from my advisors, mentors, and collaborators, especially my long-time collaborators C. Bardos, Y. Guo, E. Grenier, D. Han-Kwan, and F. Rousset, who have graciously shared with me their many insights, work, and friendship.

**Q: Could you tell us a bit about the research that won you the prize?**

**A**: I've always been fascinated by a variety of classical unsolved problems in mathematical physics such as wave turbulence and turbulence in a fluid and a plasma, where progress requires not only betting on physical intuition but also building up mathematical foundations and techniques. I shall only mention two examples.

The first example is to establish the stability of shear flows which is a central question in hydrodynamic stability dating back to classical works by Helmholtz, Kelvin, and Rayleigh who studied inviscid flows in the 19th century. Reynolds was the first to realize the importance of viscosity in understanding the transition from laminar to turbulence, which led to works in the early of the last century by Orr, Sommerfeld, Heisenberg, Tollmien, and Lin, among other prominent physicists. The fundamental conjecture was that all physical laminar flows, including those that are stable to Euler equations, are always unstable to Navier-Stokes equations at a sufficiently high Reynolds number (e.g., small viscosity), contradicting to the common belief that viscosity stabilizes the flow. The viscous destabilization phenomenon gives rise to Tollmien-Schlichting waves, which are the building block in describing the transition to turbulence in fluids and had only been formally verified through the method of matched asymptotic expansions in the physics literature.

Not until recently, a complete mathematical proof of the viscous destabilization was given in my joint work with Y. Guo and E. Grenier. This leads to my research program on boundary layers with E. Grenier which provides a rigorous roadmap towards understanding the transition from laminar to turbulent flows. Specifically, our most recent work proves the formation of smaller viscous sublayers, which do not disappear in the vanishing viscosity limit. The result in particular invalidates the classical Prandtl's boundary layer theory for unsteady Navier-Stokes flows in the inviscid limit. Notably, we develop an analytical framework that allows us to capture part of the underlying physics that was otherwise absent for high regularity data required in the previous approaches. This has led us to conjecture that the full physics would involve the formation of an infinite cascade of smaller and smaller viscous sublayers developed at the boundary.

The second example is to resolve the final state conjecture of a non-equilibrium collisionless plasma, which is widely open. Despite the absence of charged particle collisions, Landau in his 1946 seminal paper discovered a surprising damping law of plasma oscillations due to a resonant interaction between background electrons and excited particles. Landau damping is however extremely weak: the faster the electrons move, the weaker the field is damped, making it extremely elusive to be captured for nonlinear models. My research program with D. Han-Kwan, F. Rousset, E. Grenier, and I. Rodnianski is to settle this very conjecture. We have made great progress towards proving the conjecture, including a complete linear damping theory, the precise notion of Landau's law of decay, the dispersion of plasma oscillations, and the nonlinear damping of screened electrons. For confined plasmas (i.e. in the absence of long-range interactions), the fundamental damping law is phase mixing, which is exponentially strong, and my recent work with E. Grenier and I. Rodnianski not only gave an elementary proof of the celebrated Mouhot-Villani's Landau damping results, but also established the damping for a much larger class of initial data that allow highly oscillatory modes.

The research done provides foundation to many natural directions for future research in fluid dynamics and kinetic theory, and I thank SIAM again for the recognition of these lines of research.

**Q: What does your work mean to the public?**

**A**: The elementary nature of my work on Landau damping should serve as a pleasant invitation to the subject. It also provides a versatile roadmap to other applications of phase mixing and oscillations in fluids and related models. The recognition of my research also highlights the rich underlying physics and the complex mathematical subtleties in understanding the dynamics of a fluid and a plasma, which I hope will attract researchers to the field. As a matter of fact, I find research in mathematics tends to become technical and specialized rather quickly, making it hard for students and outsiders, young or old, to enter a new research subject. For this reason, I write expository articles and pedagogical lecture notes to publish on my own blog, *Snapshots in Mathematics!*, for the public.

**Q: What does being a member of SIAM mean to you?**

**A**: I appreciate the support of SIAM to the mathematics community. I emphasize the important role of SIAM in reaching out in support of researchers at all the stages of their careers and all the branches of mathematics. I have myself benefited at the early stage of my career to receive SIAM Student Travel Award in 2009 and Postdoc/Early Career SIAM Travel Award in 2011 to attend conferences and connect to the community.