Norm inflation for quadratic derivative fractional nonlinear Schrödinger equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918519712514048 |
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| author | Kondo, Toshiki Okamoto, Mamoru |
| author_facet | Kondo, Toshiki Okamoto, Mamoru |
| contents | We consider the Cauchy problem for quadratic derivative fractional nonlinear Schrödinger equations on $\mathbb{R}$ or $\mathbb{T}$. We determine the sharp exponents of the fractional derivatives for which the Cauchy problem is well-posed in the Sobolev space. Thanks to the global well-posedness result established by Nakanishi and Wang (2025), we can expand the solution as a sum of iterated terms. By deriving estimates for each iterated term, we establish norm inflation with infinite loss of regularity, which in particular implies ill-posedness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20294 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Norm inflation for quadratic derivative fractional nonlinear Schrödinger equations Kondo, Toshiki Okamoto, Mamoru Analysis of PDEs We consider the Cauchy problem for quadratic derivative fractional nonlinear Schrödinger equations on $\mathbb{R}$ or $\mathbb{T}$. We determine the sharp exponents of the fractional derivatives for which the Cauchy problem is well-posed in the Sobolev space. Thanks to the global well-posedness result established by Nakanishi and Wang (2025), we can expand the solution as a sum of iterated terms. By deriving estimates for each iterated term, we establish norm inflation with infinite loss of regularity, which in particular implies ill-posedness. |
| title | Norm inflation for quadratic derivative fractional nonlinear Schrödinger equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.20294 |