  In this paper, we will introduce the inviscid vortex stretching equation,
which is a model equation for the 3D Euler equation where the advection of
vorticity is neglected. We will show that there are smooth solutions of this
equation which blowup in finite-time, even when restricting to axisymmetric,
swirl-free solutions. This provides further evidence of the role of advection
in depleting nonlinear vortex stretching for solutions of the 3D Euler
equation.
