LJAD (Université Côte d'Azur and CNRS UMR 7351)
Wednesday, May 6th, 2026 at 3:30 CET (Paris time).
Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity
Joint work with David Gontier and Salma Lahbabi.
In this talk, I will present a non-linear model for multi-particle systems, in a bosonic regime and in an uncorrelated fermionic regime. The non-linear local self-interaction is given by a power-type nonlinearity that is supercritical near 0 and subcritical at infinity. I will show that, in both cases, the model is well-posed provided the number of particles is large enough. In particular, in the fermionic case, the model with N = 2 particles is well-posed, whereas the model with N = 1 is not.