On blowups of vorticity for the homogeneous Euler equation

Abstract

AbstractBlowups 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 () generic case the blowups of degrees at the variable time regime and of degrees 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.