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Main Author: Huang, Wenrui
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2411.02737
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author Huang, Wenrui
author_facet Huang, Wenrui
contents We study the final state problem for the Hartree equation with repulsive Coulomb potential: \[i\partial_t u+\frac{1}{2}Δu-\frac{1}{|x|}u=((-Δ)^{-1}|u|)^2u\] We show the work in \cite{KaMi} can be extended to the Hartree nonlinearity: Given a prescribed asymptotic profile, we construct a unique global solution scattering to the profile. In particular, the existence of the modified wave operators is obtained for sufficiently localized small scattering data.
format Preprint
id arxiv_https___arxiv_org_abs_2411_02737
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Modified Wave operators for the Hartree equation with repulsive Coulomb potential
Huang, Wenrui
Analysis of PDEs
We study the final state problem for the Hartree equation with repulsive Coulomb potential: \[i\partial_t u+\frac{1}{2}Δu-\frac{1}{|x|}u=((-Δ)^{-1}|u|)^2u\] We show the work in \cite{KaMi} can be extended to the Hartree nonlinearity: Given a prescribed asymptotic profile, we construct a unique global solution scattering to the profile. In particular, the existence of the modified wave operators is obtained for sufficiently localized small scattering data.
title Modified Wave operators for the Hartree equation with repulsive Coulomb potential
topic Analysis of PDEs
url https://arxiv.org/abs/2411.02737