Abstract
We prove that the modified Korteweg–de Vries equation is unconditionally well-posed in $H^s({\mathbb{T}})$ for $s\ge 1/3$. For this we gather the smoothing effect first discovered by Takaoka and Tsutsumi with an approach developed by the authors that combines the energy method, with Bourgain's type estimates, improved Strichartz estimates and the construction of modified energies.
Funding Statement
The first and third authors were partially supported by the French ANR project GEODISP. The second author was partially supported by CNPq/Brazil, grants 303051/2016–7 and 431231/2016–8.
Citation
Luc MOLINET. Didier PILOD. Stéphane VENTO. "On unconditional well-posedness for the periodic modified Korteweg–de Vries equation." J. Math. Soc. Japan 71 (1) 147 - 201, January, 2019. https://doi.org/10.2969/jmsj/76977697
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