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arXiv · 2502.04007

Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions

Takamori Kato·Kotaro Tsugawa
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Abstract

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.

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Takamori Kato, Kotaro Tsugawa. 2025-02-06. Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions. https://arxiv.org/abs/2502.04007

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