%0 Journal Article
%T On the convergence rate of the Euler-$¦Á$, an inviscid second-grade complex fluid, model to the Euler equations
%A Jasmine S. Linshiz
%A Edriss S. Titi
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s10955-009-9916-9
%X 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.
%U http://arxiv.org/abs/0911.1846v1