The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D

Mathieu Lewin (1) , Julien Sabin (1)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We consider the nonlinear Hartree equation for an interacting gas containing infinitely many particles and we investigate the large-time stability of the stationary states of the form $f(-\Delta)$, describing an homogeneous Fermi gas. Under suitable assumptions on the interaction potential and on the momentum distribution $f$, we prove that the stationary state is asymptotically stable in dimension 2. More precisely, for any initial datum which is a small perturbation of $f(-\Delta)$ in a Schatten space, the system weakly converges to the stationary state for large times.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Mathieu Lewin, Julien Sabin. The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D. Analysis & PDE, 2014, 7 (6), pp.1339-1363. ⟨10.2140/apde.2014.7.1339⟩. ⟨hal-00868782⟩