On the zero viscosity limit

P. Olesen

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arXiv · hep-th/0701237

On the zero viscosity limit

P. Olesen

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Abstract

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.

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P. Olesen. 2007-01-30. On the zero viscosity limit. https://arxiv.org/abs/hep-th/0701237

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