On blowups of vorticity for the homogeneous Euler equation

Blowups of vorticity for the three- and two-dimensional homogeneous Euler equations are studied. Two regimes of approaching a blow-up point, respectively, with variable or fixed time are analyzed. It is shown that in the n-dimensional ((Formula presented.)) generic case the blowups of degrees (Formula presented.) at the variable time regime and of degrees (Formula presented.) 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 realizable.