PANDA Project: Comprehension of the ocean, waves and their phenomena through partial differential equations, dispersive models and nonlinear analysis

In this opportunity, we talked with André de Laire, researcher of the Paradyse project team of the Inria Center at the Université of Lille, and with Claudio Muñoz, researcher of the Universidad de Chile, both coordinators of the PANDA team, who lead this initiative that allows to deepen the study on the understanding of phenomena such as tsunamis and the movement of waves on the Chilean coasts.

André de Laire: I have known Claudio for many years, and we have always shared a mathematical interest in similar problems, as well as the same kind of mathematical “tools”. However, we have never had the opportunity to collaborate. It was the arrival of Olivier Goubet on the Paradyse team at Inria that triggered the current collaboration.

Claudio Muñoz: André and I have had a strong relationship for many years. In 2019, a joint collaborator (Olivier Goubet) visited us in Chile, and we started a great collaboration on Boussinesq models (usually called “abcd” models) that has led to this joint collaboration. Then I visited them in France in 2023 and had the opportunity to meet the Paradyse team and the Inria center in Lille. This visit was extraordinary, as it was an opportunity where I learned a lot about applied research and also about science management.

André de Laire: Our objective is to study various models of dispersive partial differential equations (PDEs), based on nonlinear analysis and numerical simulation techniques.

Claudio Muñoz: Earthquakes are frequent in Chile, and strong earthquakes produce tsunamis that are difficult to model in real time. It turns out that the mathematical understanding of the motion of a tsunami wave on the Chilean coast (e.g., in the Niebla-Corral Bay near Valdivia) has not been studied in detail using applied mathematics.

Claudio Muñoz: There are several advantages, some related to research, others to communication and networking with Inria and the French research system. Firstly, we benefit from the competencies and joint work with other teams with capabilities that are not present here. Secondly, we have access to state-of-the-art techniques in pure and applied mathematics and, finally, we establish strong networks with Inria and our Chilean counterparts.

André de Laire: The main advantage is to be able to attack a problem using very different points of view, but in a very complementary way. From the French point of view, the contribution of the Chilean collaborators is very important because of their expertise on the problems we study in PANDA. Moreover, Chilean tsunamis are part of our main motivations!

Claudio Muñoz: Inria Paradyse has a great research capability in numerical and theoretical modeling of nonlinear waves. In Chile, we have been working on theoretical fluid models that build irregular solitary waves. The French PANDA team has rapidly developed a numerical approach to better understand our results on the existence of solitary waves in fluid models with slowly varying surfaces. This is the starting point of a deeper research objective, which is the understanding of real waves riding a variable surface, as is often the case in tsunamis.

André de Laire: I have long wanted to collaborate with my Chilean colleagues. However, the distance makes it quite complicated and expensive. That is why the associate team is an excellent opportunity to facilitate visits and scientific discussions. For example, thanks to the associate team, we are going to hold two workshops in 2024, one in Lille and one in Santiago.

Claudio Muñoz: It is a great opportunity to start a new area of work here in Chile, where we believe many advances can be obtained in the coming years, and with the strong support given by Inria and the Paradyse team. Partnering with a part of the Inria research network will benefit us with more research tools and techniques, and will allow us to improve our research in many directions. Young researchers will also benefit from this joint collaborative effort, and it is expected that new researchers will also be trained in this direction.