Uniform time of existence for the alpha Euler equations

We consider the α-Euler equations on a bounded three-dimensional domain with frictionless Navier boundary conditions. Our main result is the existence of a strong solution on a positive time interval, uniform in α, for α sufficiently small. Combined with the convergence result in [6], this implies convergence of solutions of the α-Euler equations to solutions of the incompressible Euler equations when α→0. In addition, we obtain a new result on local existence of strong solutions for the incompressible Euler equations on bounded three-dimensional domains. The proofs are based on new a priori estimates in conormal spaces.