Global well-posedness of Korteweg-de Vries equation in H-3/4(R)

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Abstract

We prove that the Korteweg-de Vries initial-value problem is globally well-posed in H- 3 / 4 (R) and the modified Korteweg-de Vries initial-value problem is globally well-posed in H1 / 4 (R). The new ingredient is that we use directly the contraction principle to prove local well-posedness for KdV equation in H- 3 / 4 by constructing some special resolution spaces in order to avoid some logarithmic divergence from the high-high interactions. Our local solution has almost the same properties as those for Hs (s > - 3 / 4) solution which enable us to apply the I-method to extend it to a global solution.
Original languageEnglish
Pages (from-to)583 - 597
Number of pages15
JournalJournal des Mathematiques Pures et Appliquees
Volume91
Issue number6
DOIs
Publication statusPublished - 2009
Externally publishedYes

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