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

1999/03/12 by J. Ginibre, J. GINIBRE, G. Velo +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35B40 #msc:35P25 #msc:35Q40 #msc:81U99

paper · pdf · doi:10.1142/s0129055x00000137

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

arxiv created 1999/03/12 · arxiv updated 2009/11/30

Abstract

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.

Cited by

• Modified wave operators for the defocusing cubic nonlinear Schrödinger equation in one space dimension with large scattering data
• Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

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