Global Existence and Blow-Up for the Euler-Poincaré Equations with a Class of Initial Data
摘要
In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincaré equations. By choosing a class of new and special initial data, we can transform this d-dimensional Euler-Poincaré 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.