Estimates for the Gross-Pitaevskii equation linearized around a 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_ | 1866915359795183616 |
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| author | Collot, Charles Germain, Pierre Pacherie, Eliot |
| author_facet | Collot, Charles Germain, Pierre Pacherie, Eliot |
| contents | We consider the linearized two-dimensional Gross-Pitaevskii equation around a vortex of degree one, with data in the same equivariance class. Various estimates are proved for the solution; in particular, conditions for optimal decay in $L^\infty$ and boundedness in $L^2$ are identified. The analysis relies on a full description of the spectral resolution of the linearized operator through the associated distorted Fourier transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimates for the Gross-Pitaevskii equation linearized around a vortex Collot, Charles Germain, Pierre Pacherie, Eliot Analysis of PDEs 35Q55, 35Q51, 37K40, 37K45 We consider the linearized two-dimensional Gross-Pitaevskii equation around a vortex of degree one, with data in the same equivariance class. Various estimates are proved for the solution; in particular, conditions for optimal decay in $L^\infty$ and boundedness in $L^2$ are identified. The analysis relies on a full description of the spectral resolution of the linearized operator through the associated distorted Fourier transform. |
| title | Estimates for the Gross-Pitaevskii equation linearized around a vortex |
| topic | Analysis of PDEs 35Q55, 35Q51, 37K40, 37K45 |
| url | https://arxiv.org/abs/2503.02953 |