Wave-breaking phenomena and persistence properties for the nonlocal rotation-Camassa–Holm equation
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.
KeywordsRotation-Camassa–Holm equation Blow-up Wave breaking Persistence
Mathematics Subject Classification35B30 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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