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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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