Local wellposedness of the 2d Anderson-Gross-Pitaevskii equation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911278653505536 |
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| author | Mackowiak, Samaël |
| author_facet | Mackowiak, Samaël |
| contents | In this paper, the local wellposedness of a general Gross-Pitaevskii equation with rough potential is proven in dimension 2. The class of rough potentials we are considering is large enough to contain the spatial white noise and thus a renormalization procedure may be needed. We first construct the associated Schrödinger operator from its quadratic form. Then, the regularity of elements of its domain is explored. This allows to use a paracontrolled approach in order to obtain Strichartz estimates, which are used to prove the local wellposedness by a contraction argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17063 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local wellposedness of the 2d Anderson-Gross-Pitaevskii equation Mackowiak, Samaël Analysis of PDEs Mathematical Physics Probability In this paper, the local wellposedness of a general Gross-Pitaevskii equation with rough potential is proven in dimension 2. The class of rough potentials we are considering is large enough to contain the spatial white noise and thus a renormalization procedure may be needed. We first construct the associated Schrödinger operator from its quadratic form. Then, the regularity of elements of its domain is explored. This allows to use a paracontrolled approach in order to obtain Strichartz estimates, which are used to prove the local wellposedness by a contraction argument. |
| title | Local wellposedness of the 2d Anderson-Gross-Pitaevskii equation |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2511.17063 |