The workshop will take place in Centre Inria de l’Université de Lille.
Thursday, November 7th
- 9:00-12:00 in Lille: Free discussions in Paradyse
- 12:00-13:30 in Lille: Lunch at the restaurant
- 13:30-14:30 in Lille – 9:30-10:30 in Santiago: André de Laire , Université de Lille-Inria, Mathematical Models for Shallow Waters. In this talk, we survey several PDEs that allows us to model the dynamics of fluids in several regimes.
- 14:30-15:30 In Lille – 10:30-11:30 in Santiago: Mauricio Fuentes, Universidad de Chile Tsunami Modeling: Physical and Mathematical Challenges (via zoom) Tsunamis are a series of special waves that are triggered by geological phenomena, such as earthquakes, volcanic activity, landslides, among others. The physical aspects that control the predominant wave spectrum are tightly related with the generating source. From there, wave propagation is key to analyze how energy is spreaded over the water surface and how good the models are to capture physical phenomena, like frequency dispersion. Classical mathematical frameworks are employed, such as Non-Linear Shallow Water Equations, Boussinesq-type Equations, and other simplifications of the Navier-Stokes Equations.
Friday, November 8th
- 9:00-12:00 in Lille: Free discussions in Paradyse
- 12:00-13:30 in Lille: Lunch at the restaurant
- 13:30-14:30 in Lille – 9:30-10:30 in Santiago: Quentin Chauleur (Inria) About wave turbulence In this talk we will introduce the theory of wave turbulence, which describes the nonlinear interactions of waves outside thermal equilibrium by a statistical approach, in analogy with Boltzmann’s kinetic theory of gases.This analysis aims for instance at understanding the behavior of waves propagating at the surface of the ocean, with the coexistence of waves of various wavelengths propagating in many directions. Such nonlinear waves are usually described by weakly nonlinear dispersive PDEs, such as the Schrödinger equation. In particular, I will present a new high-order uniform in time scheme which captures such multiscale behavior. This is a joint ongoing work with Antoine Mouzard, associate professor at Université Paris Nanterre.
- 14:30-15:30 In Lille – 10:30-11:30 in Santiago: Guillaume Ferriere (Inria) A review of the Logarithmic Non-Linear Schrödinger equation In this talk, I present an overview of key results related to the Logarithmic Non-Linear Schrödinger equation (logNLS), starting with a review of the Cauchy theory, including recent developments. A remarkable feature of this equation is the preservation of Gaussian functions, which provides valuable insights into the long-time dynamics of general solutions. I will first discuss the long-time behaviour in the defocusing case before turning to the focusing case. For the latter case, not only there exists a particular stationary Gaussian solution, called Gausson, but all Gaussian solutions also exhibit (almost) periodic behavior. I will highlight several important results, including the stability of the Gausson and the existence of multi-Gaussian solutions.
