On the Cauchy problem for a two-component b-family system

This paper is concerned with the Cauchy problem for a two-component b-family system. We prove that the solution map of the Cauchy problem of the b-family system is not uniformly continuous in Hs(R)×Hs−1(R)Hs(R)×Hs−1(R), s>5/2s>5/2.