M. Oliver,
The Lagrangian averaged Euler equations as the short-time inviscid limit of the Navier--Stokes equations with Besov class data in R2,
Commun. Pure Appl. Ana., 1 (2002), 221-235.

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.
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