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

Katz, Nets; Pavlović, Nataša

doi:10.1090/S0002-9947-04-03532-9

Finite time blow-up for a dyadic model of the Euler equations
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by Nets Hawk Katz and Nataša Pavlović

Trans. Amer. Math. Soc. 357 (2005), 695-708

DOI: https://doi.org/10.1090/S0002-9947-04-03532-9

Published electronically: March 12, 2004

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Abstract:

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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