Global Well-Posedness of mKdV in<i>L</i>²(𝕋, ℝ)

Abstract

ABSTRACT We show that the Miura map L 2(𝕋) → H −1(𝕋), r↦r x + r 2 is a global fold and then apply our results on global well-posedness of KdV in H −1(𝕋) to show that mKdV is globally well-posed in L 2(𝕋).