Differential and Integral Equations

The Cauchy problem for a fifth order evolution equation

Peter Byers

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Abstract

In this paper it is shown that the Cauchy problem for a fifth order modification of the Camassa-Holm equation is locally well-posed for initial data of arbitrary size in the Sobolev space $H^s(\mathbb{R})$, $s>1/4$, and globally well-posed in $H^1(\mathbb{R})$. The proof is based on appropriate bilinear estimates obtained using Fourier analysis techniques.

Article information

Source
Differential Integral Equations, Volume 16, Number 5 (2003), 537-556.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060625

Mathematical Reviews number (MathSciNet)
MR1973061

Zentralblatt MATH identifier
1031.35122

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B20: Perturbations 35G25: Initial value problems for nonlinear higher-order equations

Citation

Byers, Peter. The Cauchy problem for a fifth order evolution equation. Differential Integral Equations 16 (2003), no. 5, 537--556. https://projecteuclid.org/euclid.die/1356060625


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