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

  • Author(s): Linshiz, Jasmine S.
  • Titi, Edriss S.
  • et al.
Abstract

We study the convergence rate of the solutions of the incompressible Euler-α, an inviscid second-grade complex fluid, equations to the corresponding solutions of the Euler equations, as the regularization parameter α approaches zero. First we show the convergence in H s , s>n/2+1, in the whole space, and that the smooth Euler-α 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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