On Local Well-posedness of the Periodic Korteweg-de Vries Equation Below H-12(T)
Abstract
We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in Hs(T) for s> -23. This work creates an analogue of the mKdV result by Nakanishi, Takaoka, and Tsutsumi for KdV, extending the currently best-known result of s ≥ -12 without utilizing the theory of complete integrability.
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