A remark on global well-posedness below L^2 for the gKdV-3 equation

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.

arXiv comment6 pages

References in corpus (1)

• Global well-posedness for Schrödinger equations with derivative

Cited by in corpus (4)

• On the radius of spatial analyticity for the quartic generalized KdV equation
• Global rough solutions to the critical generalized KdV equation
• The low regularity global solutions for the critical generalized KdV equation
• On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces