On the Cauchy problem for logarithmic fractional Schr{ö}dinger equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914747782266880 |
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| author | Carles, Rémi Dong, Fangyuan |
| author_facet | Carles, Rémi Dong, Fangyuan |
| contents | We consider the fractional Schrodinger equation with a logarithmic nonlinearity, when the power of the Laplacian is between zero and one. We prove global existence results in three different functional spaces: the Sobolev space corresponding to the quadratic form domain of the fractional Laplacian, the energy space, and a space contained in the operator domain of the fractional Laplacian. For this last case, a finite momentum assumption is made, and the key step consists in estimating the Lie commutator between the fractional Laplacian and the multiplication by a monomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Cauchy problem for logarithmic fractional Schr{ö}dinger equation Carles, Rémi Dong, Fangyuan Analysis of PDEs We consider the fractional Schrodinger equation with a logarithmic nonlinearity, when the power of the Laplacian is between zero and one. We prove global existence results in three different functional spaces: the Sobolev space corresponding to the quadratic form domain of the fractional Laplacian, the energy space, and a space contained in the operator domain of the fractional Laplacian. For this last case, a finite momentum assumption is made, and the key step consists in estimating the Lie commutator between the fractional Laplacian and the multiplication by a monomial. |
| title | On the Cauchy problem for logarithmic fractional Schr{ö}dinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.06816 |