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arXiv · 2508.19779

Unconditional Uniqueness of 5th Order KP Equations

James Patterson
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Abstract

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.

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James Patterson. 2025-08-27. Unconditional Uniqueness of 5th Order KP Equations. https://arxiv.org/abs/2508.19779

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