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2001 Remarks on the blow-up of solutions for the 3-D Euler equations
Namkwon Kim
Differential Integral Equations 14(2): 129-140 (2001). DOI: 10.57262/die/1356123348


We consider a blow-up of smooth, local-in-time solutions of the 3-D incompressible Euler equations. We give a localized analogy of the Beale-Kato-Majda-type criterion that if the solution blows up in an isolated set in our sense, the blow-up is carried with the blow-up of vorticity in that set. Besides, we show that in general the blow-up process is controlled by a suitable norm of any two components of vorticity in Cartesian coordinates.


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Namkwon Kim. "Remarks on the blow-up of solutions for the 3-D Euler equations." Differential Integral Equations 14 (2) 129 - 140, 2001.


Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1161.35333
MathSciNet: MR1797382
Digital Object Identifier: 10.57262/die/1356123348

Primary: 35Q35
Secondary: 35B40 , 76B03

Rights: Copyright © 2001 Khayyam Publishing, Inc.

Vol.14 • No. 2 • 2001
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