A remark on global well-posedness below L^2 for the gKdV-3 equation
arXiv:0707.2722
Abstract
The I-method in its first version as developed by Colliander et al. is applied to prove that the Cauchy-problem for the generalised Korteweg-de Vries equation of order three (gKdV-3) is globally well-posed for large real-valued data in the Sobolev space H^s, provided s>-1/42.
6 pages