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Blow-up phenomena for the generalized FORQ/MCH equation

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Abstract

In this paper, we are concerned with the generalized FORQ/MCH equation, which includes the celebrated Fokas–Olver–Rosenau–Qiao equation (or also called the modified Camassa–Holm equation). Firstly, a priori estimates in the transport equation theory and 1-D Morse-type estimates were applied to derive a blow-up criterion. Then, we exploit the characteristic ordinary differential equation to construct a conservative property, which leads to the precise blow-up scenario. Finally, making use of the fine structure and conservation laws, we present a blow-up result for the strong solutions with respect to the initial data.

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  1. Department of Mathematics, Kunming University of Science and Technology, Kunming, 650500, Yunnan, China

    Shaojie Yang

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Yang, S. Blow-up phenomena for the generalized FORQ/MCH equation. Z. Angew. Math. Phys. 71, 20 (2020). https://doi.org/10.1007/s00033-019-1241-9

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  • DOI: https://doi.org/10.1007/s00033-019-1241-9

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