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

Kenji Nakanishi

doi:10.3934/cpaa.2002.1.237

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2002, Volume 1, Issue 2: 237-252. Doi: 10.3934/cpaa.2002.1.237

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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

Revised: July 2001

Published: June 2002

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Abstract

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.

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Mathematics Subject Classification: 35P25.

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