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June  2002, 1(2): 237-252. doi: 10.3934/cpaa.2002.1.237

Modified wave operators for the Hartree equation with data, image and convergence in the same space

Kenji Nakanishi 1,

1. 

Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

Revised  July 2001 Published  March 2002

We construct modified wave operators for the Hartree equation with the long-range potential $|x|^{-1}$ in the whole space of $(1+|x|)^{-s}L^2$ for $s>1/2$. We also have the image, strong continuity and strong asymptotic approximation in the same space. The lower bound of the weight is sharp from the scaling argument. Those maps are homeomorphic onto open subsets, which implies in particular asymptotic completeness for small data.
Keywords: scattering theory, modified wave operators., long range potential, Hartree equation.
Mathematics Subject Classification: 35P2.
Citation: Kenji Nakanishi. Modified wave operators for the Hartree equation with data, image and convergence in the same space. Communications on Pure and Applied Analysis, 2002, 1 (2) : 237-252. doi: 10.3934/cpaa.2002.1.237
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