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Blowups of vorticity for the three- and two- dimensional homogeneous Eulerequations are studied. Two regimes of approaching a blowup points,respectively, with variable or fixed time are analysed. It is shown that in the$n$-dimensional ($n=2,3$) generic case the blowups of degrees $1,..,n$ at thevariable time regime and of degrees $1/2,..,(n+1)/(n+2)$ at the fixed timeregime may exist. Particular situations when the vorticity blows while thedirection of the vorticity vector is concentrated in one or two directions arerealisable.

On blowups of vorticity for the homogeneous Euler equation