  In this paper we study the finite time blow-up problem for the axisymmetric
3D incompressible Euler equations with swirl. The evolution equations for the
deformation tensor and the vorticity are reduced considerably in this case.
Under the assumption of local minima for the pressure on the axis of symmetry
with respect to the radial variations we show that the solution blows-up in
finite time. If we further assume that the second radial derivative vanishes on
the axis, then system reduces to the form of Constantin-Lax-Majda equations,
and can be integrated explicitly.
