Global existence and blow-up for the Euler-Poincar\'{e} equations with a class of initial data

In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincar\'{e} equations. By choosing a class of new and special initial data, we can transform this d-dimensional Euler-Poincar\'{e} equations into the Camassa-Holm type equation in the real line. We first obtain some global existence results and then present a new blow-up result to the system under some different assumptions on this special class of initial data.