The strength of a pair of point vortices in an incompressible inviscid fluid in 3d can blow up in finite time

Abstract

The evolution of a pair of point vortices in whole space, subject to the inviscid Euler equations for incompressible fluid flow, is solved exactly for rotationally symmetric initial conditions. This exact solution shows that the vortex strength for a pair of point vortices can either remain stable or blow up in finite time, depending on the initial data.