## Differential and Integral Equations

### 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. in [2] is applied to prove that the Cauchy-problem for the generalized Korteweg-de Vries equation of order three (gKdV-3) is globally well-posed for large real-valued data in the Sobolev space $H^s(\mathbb R \rightarrow \mathbb R)$, provided $s>-\frac{1}{42}$.

#### Article information

Source
Differential Integral Equations Volume 20, Number 11 (2007), 1229-1236.

Dates
First available in Project Euclid: 20 December 2012

Grünrock, Axel; Panthee, Mahendra; Silva, Jorge Drumond. A remark on global well-posedness below $L^2$ for the GKDV-3 equation. Differential Integral Equations 20 (2007), no. 11, 1229--1236. https://projecteuclid.org/euclid.die/1356039286.