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

Published 22 Nov 2024 in math.AP | (2411.15069v1)

Abstract: We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in $Hs(\mathbb{T})$ 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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Authors (2)

  1. Ryan McConnell 
  2. Seungly Oh 

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