## Differential and Integral Equations

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

### A remark on global well-posedness below $L^2$ for the GKDV-3 equation

Axel Grünrock, Mahendra Panthee, and Jorge Drumond Silva

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356039286

**Mathematical Reviews number (MathSciNet)**

MR2372424

**Zentralblatt MATH identifier**

1212.35413

**Subjects**

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B65: Smoothness and regularity of solutions

#### Citation

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