On the Gross-Pitaevskii evolution linearized around the degree-one vortex
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909567998230528 |
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| author | Luhrmann, Jonas Schlag, Wilhelm Shahshahani, Sohrab |
| author_facet | Luhrmann, Jonas Schlag, Wilhelm Shahshahani, Sohrab |
| contents | We study the evolution of the Gross-Pitaevskii equation linearized around the Ginzburg-Landau vortex of degree one under equivariant symmetry. Among the main results of this work, we determine the spectrum of the linearized operator, uncover a remarkable $L^2$-norm growth phenomenon related to a zero-energy resonance, and provide a complete construction of the distorted Fourier transform at small energies. The latter hinges upon a meticulous analysis of the behavior of the resolvent in the upper and lower half-planes in a small disk around zero-energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Gross-Pitaevskii evolution linearized around the degree-one vortex Luhrmann, Jonas Schlag, Wilhelm Shahshahani, Sohrab Analysis of PDEs We study the evolution of the Gross-Pitaevskii equation linearized around the Ginzburg-Landau vortex of degree one under equivariant symmetry. Among the main results of this work, we determine the spectrum of the linearized operator, uncover a remarkable $L^2$-norm growth phenomenon related to a zero-energy resonance, and provide a complete construction of the distorted Fourier transform at small energies. The latter hinges upon a meticulous analysis of the behavior of the resolvent in the upper and lower half-planes in a small disk around zero-energy. |
| title | On the Gross-Pitaevskii evolution linearized around the degree-one vortex |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.07345 |