Journées EDP 2024 - Sciencesconf.org

9:00 - 10:30 (1h30)

Patrick Gérard -------------------- Integrable equations of Benjamin-Ono type

In this mini-course, I will study two integrable nonlinear dispersive equations on the line : the Benjamin-Ono equation and the more recently introduced Calogero-Moser derivative nonlinear Schrödinger equation. The following topics will be discussed. 1. Local wellposedness in Sobolev spaces, Lax pair, explicit formulae. 2. Conservation laws and global wellposedness. 3. Traveling waves and multi-solitons. 4. Zero-dispersion limit.

10:30 - 11:00 (30min)

Pause café

11:00 - 12:00 (1h)

Pierre Germain ----------------------- TBA

Pierre Germain

12:15 - 14:00 (1h45)

Déjeuner

15:00 - 16:00 (1h)

Ewelina Zatorska ----------------------- TBA

Ewelina Zatorska

16:00 - 16:30 (30min)

Pause café

16:30 - 17:30 (1h)

Kevin Le Balc'h ----------------------- TBA

Kevin Le Balc'h

17:30 - 18:30 (1h)

Grégory Faye ----------------------- The local limit theorem for complex valued sequences: the parabolic case.

We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in probability theory for random walks as well as in numerical analysis for studying the large time behavior of numerical schemes. This is joint work with Jean-François Coulombel.

18:30 - 19:30 (1h)

Apéritif spécial 50 ans

19:30 - 21:00 (1h30)

Dîner

Programme