Mathematical analysis of pulsatile flow, vortex breakdown and instantaneous blow-up for the axisymmetric Euler equations

2017/04/27 by Tsuyoshi Yoneda, Yoneda, Tsuyoshi
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1704.08436

openalex publication_date 2017/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Ill-posedness results in critical spaces for some equations arising in hydrodynamics

Related

• An instability mechanism of pulsatile flow along particle trajectories for the axisymmetric Euler equations
• A geometric instability of the laminar axisymmetric Euler flows with oscillating flux
• Vorticity blowup in 2D compressible Euler equations
• The strength of a pair of point vortices in an incompressible inviscid fluid in 3d can blow up in finite time
• Removing Type II singularities off the axis for the 3D axisymmetric Euler equations