Strichartz estimates for Critical magnetic Schrödinger operators on flat Euclidean cones
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910906540097536 |
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| author | Gao, Xiaofen Wang, Jialu Xu, Chengbin Zhang, Fang |
| author_facet | Gao, Xiaofen Wang, Jialu Xu, Chengbin Zhang, Fang |
| contents | In this paper, we study Schrödinger operator $\mathcal{H}_{\mathbf{A}}$ perturbed by critical magnetic potentials on the 2D flat cone $Σ= C(\mathbb{S}_ρ^1) = (0, \infty) \times \mathbb{S}_ρ^1$, which is a product cone over the circle $\mathbb{S}_ρ^1 = \mathbb{R}/2πρ\mathbb{Z}$ with radius $ρ> 0$, and equipped with the metric $g = dr^2 + r^2 dθ^2$. The goal of this work is to establish Strichartz estimates for $\mathcal{H}_{\mathbf{A}}$ in this setting. A key aspect of our approach is the construction of the Schwartz kernel of the resolvent and the spectral measure for Schrödinger operator on the flat Euclidean cone $(Σ, g)$. The results presented here generalize previous work in \cite{Ford, BFM, FZZ, Zhang1}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz estimates for Critical magnetic Schrödinger operators on flat Euclidean cones Gao, Xiaofen Wang, Jialu Xu, Chengbin Zhang, Fang Analysis of PDEs In this paper, we study Schrödinger operator $\mathcal{H}_{\mathbf{A}}$ perturbed by critical magnetic potentials on the 2D flat cone $Σ= C(\mathbb{S}_ρ^1) = (0, \infty) \times \mathbb{S}_ρ^1$, which is a product cone over the circle $\mathbb{S}_ρ^1 = \mathbb{R}/2πρ\mathbb{Z}$ with radius $ρ> 0$, and equipped with the metric $g = dr^2 + r^2 dθ^2$. The goal of this work is to establish Strichartz estimates for $\mathcal{H}_{\mathbf{A}}$ in this setting. A key aspect of our approach is the construction of the Schwartz kernel of the resolvent and the spectral measure for Schrödinger operator on the flat Euclidean cone $(Σ, g)$. The results presented here generalize previous work in \cite{Ford, BFM, FZZ, Zhang1}. |
| title | Strichartz estimates for Critical magnetic Schrödinger operators on flat Euclidean cones |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.06045 |