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Transactions of the American Mathematical Society

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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
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

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

Received by editor(s): July 25, 2003
Published electronically: March 12, 2004
Article copyright: © Copyright 2004 American Mathematical Society