PreprintCC BY 4.0arXiv
Scattering for Short-Range Mass-Subcritical Choquard Equations
Abstract
We study scattering for the defocusing inhomogeneous generalized Choquard equation with data in the conformal energy space. In the full short-range mass-subcritical regime, a key estimate for the nonlinear term yields scattering in L2. A pseudoconformal argument in the compactified variables then gives scattering in H1. In the homogeneous case, estimates based on the Galilean vector field further imply scattering in Σ above the Strauss threshold. The method avoids the additional algebraic restrictions arising from intermediate Strichartz-Sobolev estimates.
Related
- Modified wave operators for nonlinear Schrödinger equations in the full subcritical long range regime
- Scattering Across the Long-Range Threshold for One-Dimensional Nonlinear Schrödinger Equations
- Systems of Kirchhoff quasilinear Schrodinger equations with Hardy potential and critical Choquard-type nonlinearity
- A Sharp Mass Threshold for Fractional Choquard Equations with Lower Hardy-Littlewood-Sobolev and L2-Critical Terms
- Orbital stability of positive standing waves to the logarithmic Choquard equations
BibTeX
@misc{michelangeli2026scattering,
title = {{Scattering for Short-Range Mass-Subcritical Choquard Equations}},
author = {Alessandro Michelangeli and Mirko Tarulli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33775},
eprint = {2609.33775},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33775},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scattering for Short-Range Mass-Subcritical Choquard Equations
AU - Alessandro Michelangeli
AU - Mirko Tarulli
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33775
UR - https://arxiv.org/abs/2609.33775
AB - We study scattering for the defocusing inhomogeneous generalized Choquard equation with data in the conformal energy space. In the full short-range mass-subcritical regime, a key estimate for the nonlinear term yields scattering in L^2. A pseudoconformal argument in the compactified variables then gives scattering in H^1. In the homogeneous case, estimates based on the Galilean vector field further imply scattering in Σ above the Strauss threshold. The method avoids the additional algebraic restrictions arising from intermediate Strichartz-Sobolev estimates.
ER -