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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.18183 |
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Table of Contents:
- The goal of a recently launched project is to extend the Euclidean models in \cite{Wang24,WZZ25-AHP,WZZ25-JDE} to a more general setting of conically singular spaces. In this paper, the main results include a weighted dispersive inequality for the Schrödinger equation and a dispersive estimate for the wave equation both with one Aharonov-Bohm solenoid in a uniform magnetic field on the product cone $X=\mathcal{C}(\mathbb{S}_σ^1)=(0,+\infty)_r\times\mathbb{S}_σ^1$ endowed with the flat metric $g=dr^2+r^2dθ^2$, where $\mathbb{S}_σ^1\simeq\mathbb{R}/2πσ\mathbb{Z}$ denotes the circle of radius $σ\geq1$ in the Euclidean plane $\mathbb{R}^2$. As a byproduct, we also give the corresponding Strichartz estimates for these equations via the abstract argument of Keel-Tao.