Finite time blow-up for a dyadic model of the Euler equations

@article{Katz2004FiniteTB,
title={Finite time blow-up for a dyadic model of the Euler equations},
author={Nets Hawk Katz and Nata{\vs}a Pavlovi{\'c}},
journal={Transactions of the American Mathematical Society},
year={2004},
volume={357},
pages={695-708}
}
• Published 12 March 2004
• Mathematics
• Transactions of the American Mathematical Society
We introduce a dyadic model for the Euler equations and the Navier-Stokes equations with hyper-dissipation in three dimensions. For the dyadic Euler equations we prove finite time blow-up. In the context of the dyadic Navier-Stokes equations with hyper-dissipation we prove finite time blow-up in the case when the dissipation degree is sufficiently small.
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