Local well-posedness and blow-up in the energy space for the 2D NLS with point interaction
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916844199215104 |
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| author | Forcella, Luigi Georgiev, Vladimir |
| author_facet | Forcella, Luigi Georgiev, Vladimir |
| contents | We consider the two-dimensional nonlinear Schrödinger equation with point interaction and we establish a local well-posedness theory, including blow-up alternative and continuous dependence on the initial data in the energy space. We provide a proof by employing a Kato's method along with Hardy inequalities with logarithmic correction. Moreover, we establish finite time blow-up for solutions with positive energy and infinite variance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16039 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local well-posedness and blow-up in the energy space for the 2D NLS with point interaction Forcella, Luigi Georgiev, Vladimir Analysis of PDEs Mathematical Physics We consider the two-dimensional nonlinear Schrödinger equation with point interaction and we establish a local well-posedness theory, including blow-up alternative and continuous dependence on the initial data in the energy space. We provide a proof by employing a Kato's method along with Hardy inequalities with logarithmic correction. Moreover, we establish finite time blow-up for solutions with positive energy and infinite variance. |
| title | Local well-posedness and blow-up in the energy space for the 2D NLS with point interaction |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2410.16039 |