The Beale-Kato-Majda criterion is a continuation criterion for smooth solutions of the three-dimensional Euler's equations
of inviscid motion. Let 
be such a solution, let 
be its vorticity, and let 
be its maximal time of smooth existence. The solution can
be continued past a time 
provided
 |
Equivalently, finite-time blow-up at 
requires this integral to diverge as 
approaches 
. Here the 
norm is the essential
supremum over space (Beale et al. 1984).
