Communications on Pure and Applied Analysis (CPAA)

The Lagrangian averaged Euler equations as the short-time inviscid limit of the Navier–Stokes equations with Besov class data in $\mathbb{R}^2$

Pages: 221 - 235, Volume 1, Issue 2, June 2002      doi:10.3934/cpaa.2002.1.221

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Marcel Oliver - Mathematisches Institut, Universitat Tubingen, 72076 Tubingen, Germany (email)

Abstract: We compare the vorticity corresponding to a solution of the Lagrangian averaged Euler equations on the plane to a solution of the Navier–Stokes equation with the same initial data, assuming that the averaged Euler potential vorticity is in a certain Besov class of regularity. Then the averaged Euler vorticity stays close to the Navier–Stokes vorticity for a short interval of time as the respective smoothing parameters tend to zero with natural scaling.

Keywords:  Averaged Euler equations, Navier–stokes equations
Mathematics Subject Classification:  35Q30

Revised: July 2001;      Available Online: March 2002.