Cancellation properties and unconditional well-posedness for the fifth order KdV type equations with periodic boundary condition
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911882832510976 |
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| author | Kato, Takamori Tsugawa, Kotaro |
| author_facet | Kato, Takamori Tsugawa, Kotaro |
| contents | We consider the fifth order KdV type equations and prove the unconditional well-posedness in $H^s(\mathbb{T})$ for $s \ge 1$. It is optimal in the sense that the nonlinear terms can not be defined in the space-time distribution framework for $s<1$. The main idea is to employ the normal form reduction and a kinds of cancellation properties to deal with the derivative losses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_07190 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cancellation properties and unconditional well-posedness for the fifth order KdV type equations with periodic boundary condition Kato, Takamori Tsugawa, Kotaro Analysis of PDEs We consider the fifth order KdV type equations and prove the unconditional well-posedness in $H^s(\mathbb{T})$ for $s \ge 1$. It is optimal in the sense that the nonlinear terms can not be defined in the space-time distribution framework for $s<1$. The main idea is to employ the normal form reduction and a kinds of cancellation properties to deal with the derivative losses. |
| title | Cancellation properties and unconditional well-posedness for the fifth order KdV type equations with periodic boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2308.07190 |