Local well‐posedness and zero‐ α limit for the Euler‐ α equations

In this paper, we prove the local‐in‐time existence and a blow‐up criterion of solutions in the Besov spaces for the Euler‐ α equations of inviscid incompressible fluid flows inR d , d ≥ 2 . We also establish the convergence rate of the solutions of the Euler‐ α equations to the corresponding solutions of the Euler equations as the regularization parameter α approaches 0 inR 2 . Copyright © 2016 John Wiley & Sons, Ltd.