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

Authors:
Nets Hawk Katz and Natasa Pavlovic

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

MSC (2000):
Primary 35Q30, 35Q35, 76B03

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

Published electronically:
March 12, 2004

MathSciNet review:
2095627

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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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Additional Information

**Nets Hawk Katz**

Affiliation:
Department of Mathematics, Washington University, St. Louis, Missouri 63130

Email:
nets@math.wustl.edu

**Natasa Pavlovic**

Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544

Email:
natasa@math.princeton.edu

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

Received by editor(s):
July 25, 2003

Published electronically:
March 12, 2004

Article copyright:
© Copyright 2004
American Mathematical Society