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

Abstract

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.