On the zero viscosity limit
Abstract
Description
The question of whether the zero viscosity limit $ν\to 0$ is identical to the no viscosity $ν\equiv 0$ case is investigated in a simple shell (GOY) model with only three shells. We find that it is possible to express two velocities in terms of Bessel functions. The third velocity function acts as a background. The relevant Bessel functions are infinitely oscillating as $ν\to 0$ and do not have a limiting value. Therefore two of the velocity functions of this three-shell model are not analytic functions of $ν$ at the point $ν=0$. We also mention a perturbative method which may be used to improve the model.
10 pages. Some formulas have been simplified and clarifying remarks have been added
10 pages. Some formulas have been simplified and clarifying remarks have been added