Wave-breaking phenomena and persistence properties for the nonlocal rotation-Camassa–Holm equation

  • Min Zhu
  • Yue LiuEmail author
  • Yongsheng Mi


Consideration in the present paper is a mathematical model proposed as an equation of long-crested shallow water waves propagating in one direction with the effect of Earth’s rotation. This model equation is analogous to the Camassa–Holm approximation of the two-dimensional incompressible and irrotational Euler equations, and its solution corresponding to physically relevant initial perturbations is more accurate on a much longer timescale. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on the blow-up criteria and wave-breaking phenomena in the periodic setting are investigated. Moreover, working with moderate weight functions that are commonly used in time–frequency analysis, some persistence results to the equation are illustrated.


Rotation-Camassa–Holm equation Blow-up Wave breaking Persistence 

Mathematics Subject Classification

35B30 35G25 35Q53 



The authors would like to thank the referees for constructive suggestions and comments. The work of Zhu is partially supported by the NSF of China under the Grant 11401309. The work of Liu is supported partially by the Simons Foundation Grant 499875. The work of Mi is partially supported by the NSF of China-11671055, the NSF of Chongqing-cstc2018jcyjAX0273, and the key project of science and technology research program of Chongqing Education Commission (KJZD-K20180140).


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNanjing Forestry UniversityNanjingPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA
  3. 3.College of Mathematics and Computer SciencesYangtze Normal UniversityFulingPeople’s Republic of China

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