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arXiv · 1711.09720

On the existence of periodic solutions to the modified Korteweg-de Vries equation below $H^{1/2}(\mathbb{T})$

Robert Schippa
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Abstract

Existence and a priori estimates for real-valued periodic solutions to the modified Korteweg-de Vries equation with initial data in $H^s$ are established for $s>0$. The short-time Fourier restriction norm method is employed to overcome the derivative loss. Further, non-existence of solutions below $L^2$ is proved conditional upon conjectured linear Strichartz estimates.

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Robert Schippa. 2017-11-27. On the existence of periodic solutions to the modified Korteweg-de Vries equation below $H^{1/2}(\mathbb{T})$. https://doi.org/10.1007/s00028-019-00538-0

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