TY - JOUR

T1 - Global well-posedness of Korteweg-de Vries equation in H-3/4(R)

AU - Guo, Zihua

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.sciencedirect.com/science/article/pii/S0021782409000130/pdf?md5=de6d3ea150d68fd6ce3445b01d3f6f68&pid=1-s2.0-S0021782409000130-main.pdf

U2 - 10.1016/j.matpur.2009.01.012

DO - 10.1016/j.matpur.2009.01.012

M3 - Article

SN - 0021-7824

VL - 91

SP - 583

EP - 597

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 6

ER -