Open Access
January, 2019 On unconditional well-posedness for the periodic modified Korteweg–de Vries equation
Luc MOLINET, Didier PILOD, Stéphane VENTO
J. Math. Soc. Japan 71(1): 147-201 (January, 2019). DOI: 10.2969/jmsj/76977697


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.


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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.


Received: 20 December 2016; Revised: 20 July 2017; Published: January, 2019
First available in Project Euclid: 26 October 2018

zbMATH: 07056561
MathSciNet: MR3909918
Digital Object Identifier: 10.2969/jmsj/76977697

Primary: 35A02 , 35E15 , 35Q53
Secondary: 35B45 , 35D30

Keywords: modified energy , periodic modified Korteweg–de Vries equation , unconditional uniqueness , well-posedness

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 1 • January, 2019
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