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

Marcel Oliver

doi:10.3934/cpaa.2002.1.221

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2002, Volume 1, Issue 2: 221-235. Doi: 10.3934/cpaa.2002.1.221

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

Marcel Oliver^1,

1.
Mathematisches Institut, Universitat Tubingen, 72076 Tubingen

Revised: July 2001

Published: June 2002

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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.

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

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