Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916600763908096 |
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| author | Kato, Takamori Tsugawa, Kotaro |
| author_facet | Kato, Takamori Tsugawa, Kotaro |
| contents | We prove the unconditional well-posedness result for fifth order modified KdV type equations in $H^s(\mathbb{T})$ when $s \geq 3/2$, which includes non-integrable cases. By the conservation laws, we also obtain the global well-posedness result when $s = 2$, which also includes non-integrable cases. The main idea is to employ the normal form reduction and a kind of cancellation properties to deal with the derivative losses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_04007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions Kato, Takamori Tsugawa, Kotaro Analysis of PDEs We prove the unconditional well-posedness result for fifth order modified KdV type equations in $H^s(\mathbb{T})$ when $s \geq 3/2$, which includes non-integrable cases. By the conservation laws, we also obtain the global well-posedness result when $s = 2$, which also includes non-integrable cases. The main idea is to employ the normal form reduction and a kind of cancellation properties to deal with the derivative losses. |
| title | Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.04007 |