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Modified wave operators for the Hartree equation with data, image and convergence in the same space. II. (English) Zbl 1040.35054

The author constructs the modified wave operators for Hartree equations with long-range interactions \(| x|^{-\nu}\). He extends his previous results [see Part I, Commun. Pure appl. Anal. 1, 237–252 (2002; Zbl 1013.35056)] to the whole range of the Dollard type \(1/2 < \nu < 1\). His results imply, in particular, asymptotic completeness for small data.

MSC:

35P25 Scattering theory for PDEs
35Q40 PDEs in connection with quantum mechanics
35B40 Asymptotic behavior of solutions to PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U99 Quantum scattering theory

Citations:

Zbl 1013.35056
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