## Advances in Differential Equations

### Classical solutions of the generalized Camassa-Holm equation

#### Abstract

In this paper, well-posedness in $C^1(\mathbb R)$ (a.k.a. classical solutions) for a generalized Camassa-Holm equation (g-$k$$b$CH) having $(k+1)$-degree nonlinearities is shown. This result holds for the Camassa-Holm, the Degasperis-Procesi and the Novikov equations, which improves upon earlier results in Sobolev and Besov spaces.

#### Article information

Source
Adv. Differential Equations, Volume 22, Number 5/6 (2017), 339-362.

Dates
First available in Project Euclid: 18 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1489802454

Mathematical Reviews number (MathSciNet)
MR3625591

Zentralblatt MATH identifier
1364.35310

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

#### Citation

Holmes, John; Thompson, Ryan C. Classical solutions of the generalized Camassa-Holm equation. Adv. Differential Equations 22 (2017), no. 5/6, 339--362. https://projecteuclid.org/euclid.ade/1489802454