Mathematical Physics, Analysis and Geometry

, Volume 15, Issue 4, pp 317–329 | Cite as

On a Shallow Water Equation Perturbed in Schwartz Class

  • Xiang’ou ZhuEmail author


We discuss the Camassa-Holm equation perturbed in Schwartz class around a suitable constant. This paper is concerned with the wave breaking mechanism for periodic case where two special classes of initial data were involved. The asymptotic behavior of solutions is also analyzed in the following sense: the corresponding solution to initial data with algebraic decay at infinity will retain this property at infinity in its lifespan.


The Camassa-Holm equation Singularity Asymptotic behavior 

Mathematics Subject Classifications (2010)

37L05 35Q58 35L30 35Q35 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.College of Physics and Electronic Information EngineeringWenzhou UniversityWenzhouChina
  2. 2.The Key Laboratory of Low-voltage Apparatus IntellectualTechnology of ZhejiangWenzhouChina

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