Long Range Scattering and Modified Wave Operators for some Hartree Type Equations II

Details Long Range Scattering and Modified Wave Operators for some Hartree Type Equations II Long Range Scattering and Modified Wave Operators for some Hartree Type Equations II

1999-03-12

arxiv.org/abs/math/9903073v1

Mathematics

Analysis of PDEs

TeX, 55 pages, available http://qcd.th.u-psud.fr

Scientific paper

10.1142/S0129055X00000137

We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma}. For 0 < gamma < or =1 we prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators,thereby extending the results of a previous paper with the same title (math.AP/9807031) which covered the range 1/2 < gamma <1.

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