The Cauchy problem for a fifth order evolution equation

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.