Long range scattering and modified wave operators for some Hartree type equations. II. (English) Zbl 1024.35084

Ginibre, J.; Velo, G.

Ann. Henri Poincaré 1, No. 4, 753-800 (2000).

The authors study the scattering theory for a class of Hartree type equations with long range interactions in space dimension \(n \geq 3\), including Hartree equations with potential \(V(x)=\lambda |x|^{-\gamma}, 0 < \gamma \leq 1\). They prove the existence of modified wave operators. The asymptotic behaviour in time of solutions in the range of the wave operators is also investigated.
For Part I, cf. Rev. Math. Phys. 12, 361-429 (2000; Zbl 1044.35041).

Reviewer: Michael Perelmuter (Kyïv)

MSC:

35P25	Scattering theory for PDEs
81U99	Quantum scattering theory
35B40	Asymptotic behavior of solutions to PDEs
35Q40	PDEs in connection with quantum mechanics

Keywords:

existence; asymptotic behaviour

Citations:

Zbl 1044.35041