Scattering Theory in the Energy Space for a Class of Hartree Equations

1998/09/30 by J. Ginibre, G. Velo, Ginibre, J. +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35B40 #msc:35P25 #msc:35Q40 #msc:81U99

paper · pdf · doi:10.48550/arxiv.math/9809183

TeX, 41 pages, available http://qcd.th.u-psud.fr

arxiv created 1998/09/30 · arxiv updated 2009/11/30

Abstract

We study the theory of scattering in the energy space for the Hartree equation in space dimension n>2. Using the method of Morawetz and Strauss, we prove in particular asymptotic completeness for radial nonnegative nonincreasing potentials satisfying suitable regularity properties at the origin and suitable decay properties at infinity. The results cover in particular the case of the potential |x|^(- gamma) for 2 < gamma < Min(4,n).

Cited by

• Dispersive estimates and long-time validity for Bogoliubov dynamics of interacting Bose gases
• Global dynamics above the ground state for the energy-critical Hartree equation with radial data

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