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A Physical-Space Approach to Modified Scattering for the 3D Hartree Equation: Full-Space and Robin Half-Space
Abstract
We prove global well-posedness and modified scattering for the three-dimensional Hartree equation for small data in H0,k, with k>1/2 on ℝ3 and k=1 on the half-space ℝ3+ with a real Robin boundary condition. For these data, the nonlinear and asymptotic analysis is carried out entirely in physical space, combining slow-growth estimates for Galilean vector fields with a scale-invariant interaction estimate. For the half-space problem, we construct an extension intertwining the Robin and free flows and a boundary-adapted field that overcome the loss of normal Galilean symmetry.
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BibTeX
@misc{pausader2026physicalspace,
title = {{A Physical-Space Approach to Modified Scattering for the 3D Hartree Equation: Full-Space and Robin Half-Space}},
author = {Benoît Pausader and Mengyi Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21002},
eprint = {2610.21002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21002},
}
RIS
TY - UNPB
TI - A Physical-Space Approach to Modified Scattering for the 3D Hartree Equation: Full-Space and Robin Half-Space
AU - Benoît Pausader
AU - Mengyi Xie
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.21002
UR - https://arxiv.org/abs/2610.21002
AB - We prove global well-posedness and modified scattering for the three-dimensional Hartree equation for small data in H^0,k, with k>1/2 on ℝ^3 and k=1 on the half-space ℝ^3_+ with a real Robin boundary condition. For these data, the nonlinear and asymptotic analysis is carried out entirely in physical space, combining slow-growth estimates for Galilean vector fields with a scale-invariant interaction estimate. For the half-space problem, we construct an extension intertwining the Robin and free flows and a boundary-adapted field that overcome the loss of normal Galilean symmetry.
ER -