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On the Cauchy problem of a three-component Camassa--Holm equations

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  • The present paper is mainly concerned with the well-posedness, blow-up phenomena and exponential decay of solution. The well-posedness for a three-component Camassa--Holm equation is established in a critical Besov space. Comparing with the result of Hu, ect. in the paper [25], a new wave-breaking solution is obtained. The exponential decay of solution in our paper covers and extents the corresponding results in [12,24,31].
    Mathematics Subject Classification: 35G25, 35L05.


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