On the Convergence Rate of the Euler-α, an Inviscid Second-Grade Complex Fluid, Model to the Euler Equations

We study the convergence rate of the solutions of the incompressible Euler-alpha, an inviscid second-grade complex fluid, equations to the corresponding solutions of the Euler equations, as the regularization parameter alpha approaches zero. First we show the convergence in H (s) , s > n/2+1, in the whole space, and that the smooth Euler-alpha solutions exist at least as long as the corresponding solution of the Euler equations. Next we estimate the convergence rate for two-dimensional vortex patch with smooth boundaries.