On unconditional well-posedness for the periodic modified Korteweg–de Vries equation

Luc Molinet; Didier Pilod; Stéphane Vento

doi:10.2969/jmsj/76977697

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

On unconditional well-posedness for the periodic modified Korteweg–de Vries equation

Luc Molinet, Didier Pilod, Stéphane Vento

著者情報

キーワード: periodic modified Korteweg–de Vries equation, unconditional uniqueness, well-posedness, modified energy

ジャーナルフリー

2019 年 71 巻 1 号 p. 147-201

DOI https://doi.org/10.2969/jmsj/76977697

詳細

抄録

We prove that the modified Korteweg–de Vries equation is unconditionally well-posed in 𝐻^𝑠(𝕋) for 𝑠 ≥ 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.