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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.02737 |
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| _version_ | 1866910685513908224 |
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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 |