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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.19779 |
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| _version_ | 1866911125281439744 |
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| author | Patterson, James |
| author_facet | Patterson, James |
| contents | In this paper we study the $5$th Order Kadomstev-Petviashvili (KP) equations posed on the real line. In particular we adapt the energy estimate argument from Guo-Molinet (arXiv:2404.12364v1 [math.AP]) to conclude unconditional uniqueness of the solution to data map for $5$th order KP type equations. Applying short-time $X^{s,b}$ methods to improve classical energy estimates provides more than sufficient decay when considering estimates on the interior of the time interval $[0,T]$. The issue is how we deal with the boundary. By abusing symmetry we can apply multilinear interpolation to gain access to $L^4$ Strichartz estimates, which provide improved derivative gain. When taken together, the regularity of our resultant function space can be arbitrarily close to $L^2$, which in the context of unconditional uniqueness results is almost sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unconditional Uniqueness of 5th Order KP Equations Patterson, James Analysis of PDEs In this paper we study the $5$th Order Kadomstev-Petviashvili (KP) equations posed on the real line. In particular we adapt the energy estimate argument from Guo-Molinet (arXiv:2404.12364v1 [math.AP]) to conclude unconditional uniqueness of the solution to data map for $5$th order KP type equations. Applying short-time $X^{s,b}$ methods to improve classical energy estimates provides more than sufficient decay when considering estimates on the interior of the time interval $[0,T]$. The issue is how we deal with the boundary. By abusing symmetry we can apply multilinear interpolation to gain access to $L^4$ Strichartz estimates, which provide improved derivative gain. When taken together, the regularity of our resultant function space can be arbitrarily close to $L^2$, which in the context of unconditional uniqueness results is almost sharp. |
| title | Unconditional Uniqueness of 5th Order KP Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.19779 |