Norm inflation for a higher-order nonlinear Schr\'odinger equation with a derivative on the circle
| Autor: | Kondo, Toshiki, Okamoto, Mamoru |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider a periodic higher-order nonlinear Schr\"odinger equation with the nonlinearity $u^k \partial_x u$, where $k$ is a natural number. We prove the norm inflation in a subspace of the Sobolev space $H^s(\mathbb{T})$ for any $s \in \mathbb{R}$. In particular, the Cauchy problem is ill-posed in $H^s(\mathbb{T})$ for any $s \in \mathbb{R}$. Comment: 16 pages |
| Databáze: | arXiv |
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