Title: Mathematical analysis of pulsatile flow, vortex breakdown and instantaneous blow-up for the axisymmetric Euler equations,
Abstract: The dynamics along the particle trajectories for the 3D axisymmetric Euler
equations are considered. It is shown that if the inflow is rapidly increasing
(pushy) in time, the corresponding laminar profile of the incompressible Euler
flow is not (in some sense) stable provided that the swirling component is not
zero. It is also shown that if the vorticity on the axis is not zero (with some
extra assumptions), then there is no steady flow. We can rephrase these
instability to an instantaneous blow-up. In the proof, Frenet-Serret formulas
and orthonormal moving frame are essentially used.