Mathematical Physics, Analysis and Geometry

, Volume 14, Issue 2, pp 101–114

Persistence Properties and Unique Continuation of Solutions to a Two-component Camassa–Holm Equation


DOI: 10.1007/s11040-011-9089-z

Cite this article as:
Guo, Z. & Ni, L. Math Phys Anal Geom (2011) 14: 101. doi:10.1007/s11040-011-9089-z


We will consider a two-component Camassa–Holm system which arises in shallow water theory. The present work is mainly concerned with persistence properties and unique continuation to this new kind of system, in view of the classical Camassa–Holm equation. Firstly, it is shown that there are three results about these properties of the strong solutions. Then we also investigate the infinite propagation speed in the sense that the corresponding solution does not have compact spatial support for t > 0 though the initial data belongs to \(C_{0}^{\infty}(\Bbb{R})\).


Two-component Camassa–Holm equationPersistence propertiesPropagation speed

Mathematics Subject Classifications (2010)


Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghaiChina
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaChina