# Geometric constraints on potentially singular solutions for the 3-D Euler equations

@article{Constantin1996GeometricCO,
title={Geometric constraints on potentially singular solutions for the 3-D Euler equations},
author={Peter Constantin and Charles Fefferman and Andrew J. Majda},
journal={Communications in Partial Differential Equations},
year={1996},
volume={21}
}
• Published 31 December 1996
• Mathematics
• Communications in Partial Differential Equations
We discuss necessary and sufficient conditions for the formation of finite time singularities (blow up) in the incompressible three dimensional Euler equations. The well-known result of Beale, Kato and Majda states that these equations have smooth solutions on the time interval (0,t) if, and only if lim/t{r_arrow}T {integral}{sup t}{sub 0} {parallel}{Omega}({center_dot},s){parallel}{sub L}{sup {infinity}} (dx)dx < {infinity} where {Omega} = {triangledown} X u is the vorticity of the fluid and u…
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