We discuss the three-dimensional Navier-Stokes equations in the presence of the axisymmetric linear strain, where the strain rate depends on time in a specific manner. It is known that the system admits solutions which blow up in finite time and whose profiles are in a backward self-similar form of the familiar Burgers vortices.
In this talk it is shown that the existing stability theory of the Burgers vortex leads to the stability of these blow-up solutions as well.
The secondary blow-up is also observed when the strain rate is relatively weak.
Joint work with Christophe Prange (Universite de Bordeaux) and Hideyuki Miura (Tokyo Institute of Technology).