The Lagrangian averaged Euler equations as the short-time inviscid limit of the Navier-Stokes equations with Besov class data in \(\mathbb{R}^2\) (Q1848480)

The author makes a study of the Lagrangian averaged Euler equations as the short-time inviscid limit \((v\to 0)\) of the Navier-Stokes equations with Besov class data in \(\mathbb{R}^2\). The main result deals with a comparison of the vorticity corresponding to a solution of the Lagrangian averaged Euler equations on \(\mathbb{R}^2\) to a solution of the Navier-Stokes equation with the same initial data. It is shown that the averaged potential vorticity close to the Navier-Stokes vorticity for a short time as the respective smoothing parameters tend to zero with natural scaling \(\alpha= \sqrt v\), where \(v\) is the kinematic viscosity of the fluid. The author also gives estimates of the \(L^2\) difference between the Navier-Stokes velocity and the averaged Euler velocity field, and the \(L^2\) difference between the averaged Euler vorticity and the Navier-Stokes vorticity.