Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 138, Issue 1-3, Pages 305-332Publisher
SPRINGER
DOI: 10.1007/s10955-009-9916-9
Keywords
Inviscid regularization of Euler equations; Euler-alpha; Second-grade non-Newtonian fluid; Vortex patch
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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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