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arXiv · 2411.15069

On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below $H^{-\frac{1}{2}}(\mathbb{T})$

Ryan McConnell·Seungly Oh
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Abstract

We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in $H^s(\mathbb{T})$ for $s> -\frac23$. This work creates an analogue of the mKdV result by Nakanishi, Takaoka, and Tsutsumi for KdV, extending the currently best-known result of $s \geq -\frac12$ without utilizing the theory of complete integrability.

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Ryan McConnell, Seungly Oh. 2024-11-22. On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below $H^{-\frac{1}{2}}(\mathbb{T})$. https://arxiv.org/abs/2411.15069

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