On the Convergence Rate of the Euler-alpha, an Inviscid Second-Grade Complex Fluid, Model to the Euler Equations
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We study the convergence rate of the solutions of the incompressible Euler-, an inviscid second-grade complex fluid, equations to the corresponding solutions of the Euler equations, as the regularization parameter approaches zero. First we show the convergence in Hs, s>n/2+1, in the whole space, and that the smooth Euler- 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. The Author(s) 2010.