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On unconditional well-posedness for the periodic modified Korteweg-de Vries equation. (English) Zbl 1416.35233

Summary: 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 H. Takaoka and Y. Tsutsumi [Int. Math. Res. Not. 2004, No. 56, 3009–3040 (2004; Zbl 1154.35442)] 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.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35E15 Initial value problems for PDEs and systems of PDEs with constant coefficients
35B45 A priori estimates in context of PDEs
35D30 Weak solutions to PDEs

Citations:

Zbl 1154.35442
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