Dispersive and Strichartz estimates for Dirac equation in a cosmic string spacetime
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910789575639040 |
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| author | D'Ancona, Piero Yin, Zhiqing Zhang, Junyong |
| author_facet | D'Ancona, Piero Yin, Zhiqing Zhang, Junyong |
| contents | In this work we study the Dirac equation on the cosmic string background, which models a one--dimensional topological defect in the spacetime. We first define the Dirac operator in this setting, classifying all of its selfadjoint extensions, and we give an explicit kernel for the propagator. Secondly, we prove dispersive estimates for the flow, with and without weights. Finally, we prove Strichartz estimates for the flow in a sharp restricted set of indices, which are different from the classical Euclidean ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10850 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dispersive and Strichartz estimates for Dirac equation in a cosmic string spacetime D'Ancona, Piero Yin, Zhiqing Zhang, Junyong Analysis of PDEs Mathematical Physics In this work we study the Dirac equation on the cosmic string background, which models a one--dimensional topological defect in the spacetime. We first define the Dirac operator in this setting, classifying all of its selfadjoint extensions, and we give an explicit kernel for the propagator. Secondly, we prove dispersive estimates for the flow, with and without weights. Finally, we prove Strichartz estimates for the flow in a sharp restricted set of indices, which are different from the classical Euclidean ones. |
| title | Dispersive and Strichartz estimates for Dirac equation in a cosmic string spacetime |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2501.10850 |