  Blowups of vorticity for the three- and two- dimensional homogeneous Euler
equations 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 the
variable time regime and of degrees $1/2,..,(n+1)/(n+2)$ at the fixed time
regime may exist. Particular situations when the vorticity blows while the
direction of the vorticity vector is concentrated in one or two directions are
realisable.
