Abstract.
We show that a smooth solution of the 3-D Euler equations in a bounded domain breaks down, if and only if a certain norm of vorticity blows up at the same time. Here the norm introduced by Yudovich, is weaker than \(L^{\infty}\)-norm and generates a Banach space including singularities of log log 1/|x|. Roughly speaking, when a smooth solution breaks down, the vorticity has stronger singularities than log log 1/|x| or has infinite number of singularities.
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Received: February 3, 2002
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Ogawa, T., Taniuchi, Y. A Note on Blow-Up Criterion to the 3-D Euler Equations in a Bounded Domain. J. math. fluid mech. 5, 17–23 (2003). https://doi.org/10.1007/s000210300001
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DOI: https://doi.org/10.1007/s000210300001