Modified wave operators for the Hartree equation with data, image and convergence in the same space
As is well known the wave operators do not exist for the Hartree equation with long-range potential \(|x|^{-1}\), i.e., the nontrivial solutions do not approach to any free solutions as time goes to plus and minus infinity. In this paper the author constructs appropriately modified wave operators that are defined on the space \( (1+|x|)^{-s} L^2, s > 1/2\). The results imply, in particular, asymptotic completeness for small data.
scientific article; zbMATH DE number 1833242