On the convergence rate of the Euler-$α$, an inviscid second-grade complex fluid, model to the Euler equations

Details On the convergence rate of the Euler-$α$, an inviscid second-grade complex fluid, model to the Euler equations On the convergence rate of the Euler-$α$, an inviscid second-grade complex fluid, model to the Euler equations

2009-11-10

arxiv.org/abs/0911.1846v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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