On the zero viscosity limit

The question of whether the zero viscosity limit ν → 0 is identical to the no viscosity ν ≡ 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 → 0 and are not analytic as functions of ν at the point ν = 0. We also mention a perturbative method which may be used to improve the model. ∗Also at the Institute for Advanced Cycling, Blegdamsvej 19, Copenhagen, Denmark