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

2008/10/31 by Zihua Guo · 1 citation
Mathematics · #math.AP #msc:35Q53

paper · pdf

published as J. Math. Pures Appl. 91 (2009) 583-597 · 20 pages, 0 figure

arxiv created 2009/04/20 · arxiv updated 2010/07/27

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 H^1/4(\R). The new ingredient is that we use directly the contraction principle to prove local well-posedness for KdV equation at s=-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 H^s (s>-3/4) solution which enable us to apply the I-method to extend it to a global solution.

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