TURBULENT·E·S

Titres et résumés - Titles and abstracts

1. Weak turbulence beyond the Euclidean case

Pierre Germain

5/23/24, 10:00 AM

The theory of weak turbulence has seen much progress recently, in particular regarding the derivation of kinetic models. However, most of the literature, be it physical or mathematical, relies on Euclidean Fourier analysis. Since many interesting physical experiments or observations are set on more general domains, it is of interest to extend the theory in this direction - but the ...

2. Turbulence at the Kolmogorov scale

Bérengère Dubrulle

5/23/24, 11:15 AM

If you stir strongly enough a viscous flow, it becomes turbulent and displays vortices and coherent structures of various sizes. The typical scale for energy dissipation is called the Kolmogorov scale η and marks the transition between the power law behavior and a steep exponential decay in the wavenumber range. Therefore, scales smaller than η contains a negligible fraction of the kinetic...

7. Wave kinetic theory for the forced/dissipated NLS equation

Ricardo Grande

5/23/24, 1:30 PM

We will present some recent developments in the justification of kinetic equa- tions in the presence of forcing and dissipation. Such settings are of particular physical relevance as they allow the study of cascades: the transfer of energy from large scales to small scales. In this talk, we provide the first rigorous justification of such a kinetic equation in the case of a wave system...

3. Flow of incompressible turbulent-like rough vector fields

Laurent Chevillard

5/23/24, 2:45 PM

I will begin with recalling some key ingredients of the phenomenology of three- dimensional fluid turbulence, both in the Eulerian framework and in its Lagrangian coun- terpart. It will be the occasion for us to define so-called fractional Gaussian fields: they are random representation of statistically homogeneous Hölder-continuous functions, and can be considered as a simplistic...

10. Large population limit for interacting particle systems on weighted graphs

Nathalie Ayi

5/23/24, 4:00 PM

When studying interacting particle systems, two distinct categories emerge: indistinguishable systems, where particle identity does not influence system dynamics, and non-exchangeable systems, where particle identity plays a significant role. One way to conceptualize these second systems is to see them as particle systems on weighted graphs. In this talk, we focus on the latter category....

9. On linearisation around singular Rayleigh-Jeans for the 4-waves kinetic equation

Angeliki Menegaki

5/24/24, 10:00 AM

We consider the 4-waves spatial homogeneous kinetic equation arising in weak wave turbulence theory. In this talk I will present some new results on the existence and behaviour of solutions around different Rayleigh-Jeans (RJ) thermodynamic equilibrium solutions. In particular, I will discuss existence of global solutions in L2 around RJ with positive chemical potential, for confined...

4. Scattering, random phase and wave turbulence

Antoine Mouzard

5/24/24, 11:15 AM

The theory of wave turbulence aims at a description of the nonlinear interaction of a large number of waves. In this talk, I will present a family of initial data for the cubic two-dimensional nonlinear Schrödinger equation on the real plane, motivated by the link between regularity of the resonant manifold and dispersive properties of the equation and scattering phenomena. These initial data...

5. Fractional diffusion approximation for kinetic equations

Marjolaine Puel

5/24/24, 1:30 PM

After a short introduction to kinetic equations, I will explain the principle of diffusion approximation which justifies the fact that the solution of a kinetic equation is approximated by an equilibrium profile with a density satisfying a macroscopic equation. I will then focus on the Fokker Planck equation with heavy tail equilibrium handled by a spectral method.

6. Landau’s currents in kinetic theory, applications to wave turbulence

François Golse

5/24/24, 2:45 PM

In his 1936 paper on collisions between charged particles subject to the Coulomb potential, Landau introduced a current whose divergence is the collision integral. This talk discusses applications of Landau’s idea to some classical notions in wave turbulence, such as Kolmogorov-Zakharov profiles (Work with M. Escobedo and L. Saint-Raymond).

8. Large Population Limit for Interacting Particle Systems on Weighted Graphs

Nathalie Ayi

When studying interacting particle systems, two distinct categories emerge: indistinguishable systems, where particle identity does not influence system dynamics, and non-exchangeable systems, where particle identity plays a significant role. One way to conceptualize these second systems is to see them as particle systems on weighted graphs. In this talk, we focus on the latter category....