Abstract:

This article considers a family of 3D-Hartree-type equation with Coulomb potential |x|^-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.

Key words: Hartree equation, geometric optics, Lagrangian integral