Global conservative solution for the periodic $\mu$-Camassa-Holm equation

Abstract

In this paper we mainly investigate the periodic $\mu$-Camassa-Holm equation. We show the existence of global conservative solutions to the Cauchy problem of the periodic $\mu$-Camassa-Holm equation. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. Our solutions depend continuously on the initial data and has a semigroup property.

This paper has been withdrawn by the author due to a similar result has been published

References in corpus (1)

• Blow-up solutions and peakons to a generalized $\mu$-Camassa-Holm integrable equation