Differential and Integral Equations

Remarks on the blow-up of solutions for the 3-D Euler equations

Namkwon Kim

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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.

Article information

Differential Integral Equations, Volume 14, Number 2 (2001), 129-140.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35B40: Asymptotic behavior of solutions 76B03: Existence, uniqueness, and regularity theory [See also 35Q35]


Kim, Namkwon. Remarks on the blow-up of solutions for the 3-D Euler equations. Differential Integral Equations 14 (2001), no. 2, 129--140. https://projecteuclid.org/euclid.die/1356123348

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