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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.08564 |
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| _version_ | 1866914171504820224 |
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| author | Guérin, Anatole |
| author_facet | Guérin, Anatole |
| contents | The aim of this article is to prove the existence of a new class of solutions of 1D cubic NLS with an initial data related to a sum of Dirac masses, of critical regularity $F(L^\infty)$, and belonging to $\dot H^s$ for any $s <-1/2$. This problem is motivated by the lack of result for critical regularity initial condition. Our result is based on a scattering approach, after performing a pseudo-conformal transformation, and on fine estimations of oscillatory integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08564 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new class of critical solutions for 1D cubic NLS Guérin, Anatole Analysis of PDEs The aim of this article is to prove the existence of a new class of solutions of 1D cubic NLS with an initial data related to a sum of Dirac masses, of critical regularity $F(L^\infty)$, and belonging to $\dot H^s$ for any $s <-1/2$. This problem is motivated by the lack of result for critical regularity initial condition. Our result is based on a scattering approach, after performing a pseudo-conformal transformation, and on fine estimations of oscillatory integrals. |
| title | A new class of critical solutions for 1D cubic NLS |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2212.08564 |