On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations

TL;DR

This paper demonstrates that simplified 1D models inspired by the 3D axisymmetric Euler equations can develop finite-time singularities from smooth initial conditions, shedding light on potential boundary singularities.

Contribution

It introduces and analyzes 1D boundary models for 3D Euler equations, showing they can blow up in finite time, advancing understanding of singularity formation.

Findings

Models exhibit finite-time blow-up from smooth data

Supports the possibility of boundary singularities in 3D Euler equations

Provides a simplified framework for studying singularity formation

Abstract

In connection with the recent proposal for possible singularity formation at the boundary for solutions of 3d axi-symmetric incompressible Euler's equations (Luo and Hou, 2013), we study models for the dynamics at the boundary and show that they exhibit a finite-time blow-up from smooth data.