In this paper,blow-up criterions and global solutions of the Cauchy problem for the following five-order Camassa-Holm equation is studied yt+2uxy+uyx=0,y=(1-∂2x)2u.Using the the special structure of the model and the H2 conservation law,we estibalish two blow-up criterions in Bsp,r with s＞max{7/2,3+1/p},i.e,the integral of the ||u||w2,∞ or ||uxx||L∞ with respect to the lifespan blow up.And two sufficient conditions for the existence of global solutions are established by the blow-up criterions.
维普
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