Semiclassical analysis for Hartree equation

Article type: Research Article

Authors: Carles, Rémi | Masaki, Satoshi

Affiliations: CNRS & Université Montpellier 2, Mathématiques, CC 051, Place Eugène Bataillon, 34095 Montpellier cedex, France. E-mail: Remi.Carles@math.cnrs.fr | Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan. E-mail: machack@math.kyoto-u.ac.jp

Abstract: We justify WKB analysis for Hartree equation in space dimension at least three, in a régime 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 Schrödinger equation with a local nonlinearity, where quasilinear analysis is needed to treat the nonlinearity.

Keywords: Hartree equation, WKB analysis, Zhidkov spaces, instability

DOI: 10.3233/ASY-2008-0882

Journal: Asymptotic Analysis, vol. 58, no. 4, pp. 211-227, 2008