Semiclassical Analysis for Hartree equation

Details Semiclassical Analysis for Hartree equation Semiclassical Analysis for Hartree equation

2007-12-11

arxiv.org/abs/0712.1679v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

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.

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