Semiclassical Analysis for Hartree equation

Rémi Carles (1) , Satoshi Masaki (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 Kyoto - Department of Mathematics, Kyoto University

We justify WKB analysis for Hartree equation in space dimension at least three, in a regime which is supercritical as far as semiclassical analysis is concerned. The main technical remark is that the nonlinear Hartree term can be considered as a semilinear perturbation. This is in contrast with the case of the nonlinear Schrodinger equation with a local nonlinearity, where quasilinear analysis is needed to treat the nonlinearity.

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

Rémi Carles, Satoshi Masaki. Semiclassical Analysis for Hartree equation. Asymptotic Analysis, 2008, 58 (4), pp.211-227. ⟨10.3233/ASY-2008-0882⟩. ⟨hal-00195618⟩