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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.18183 |
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| _version_ | 1866914212078419968 |
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| author | Wang, Haoran |
| author_facet | Wang, Haoran |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field III: Product cones Wang, Haoran Analysis of PDEs 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. |
| title | Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field III: Product cones |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.18183 |