Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation

@article{Luo2014TowardTF,
title={Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation},
author={Guo Luo and Thomas Y. Hou},
journal={Multiscale Modeling & Simulation},
year={2014},
volume={12},
pages={1722-1776}
}

Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by presenting a class of potentially singular solutions to the Euler equations computed in axisymmetric geometries. The solutions satisfy a periodic boundary condition along the axial direction… CONTINUE READING