Unconditional uniqueness for the modified Korteweg-de Vries equation on the line

2014/11/20 by Molinet, Luc, Pilod, Didier, Vento, Stéphane · 1 citation
#35A02 #35B45 #35D30 #35E15 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.5707

Abstract

We prove that the modified Korteweg- de Vries equation (mKdV) equation is unconditionally well-posed in H^s(\mathbb R) for s> \frac 13. Our method of proof combines the improvement of the energy method introduced recently by the first and third authors with the construction of a modified energy. Our approach also yields a priori estimates for the solutions of mKdV in H^s(\mathbb R), for s>0, and enables us to construct weak solutions at this level of regularity.

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