Abstract
In this paper, we mainly devote to investigate the generalized Camassa–Holm equation with dual-power nonlinearities. We first establish the local well-posedness by applying the Kato’s semigroup theory. Then, the precise blow-up result is obtained by using the transport equation theory and Moser-type estimates. Moreover, according to the different real-valued intervals in which the dispersive parameter s is located, the sufficient conditions which guarantee the occurrence of wave-breaking of solutions are studied. It is worth noting that we need to overcome the difficulty caused by complicated mixed dual-power nonlinear structure and balance the relationship between the various dispersive parameters to get corresponding convolution estimates.
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