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We study the three-dimensional Navier-Stokes equations in the presence of theaxisymmetric linear strain, where the strain rate depends on time in a specificmanner. It is known that the system admits solutions which blow up in finitetime and whose profiles are in a backward self-similar form of the familiarBurgers vortices. In this paper it is shown that the existing stability theoryof the Burgers vortex leads to the stability of these blow-up solutions aswell. The secondary blow-up is also observed when the strain rate is relativelyweak.

On stability of blow-up solutions of the Burgers vortex type for the Navier-Stokes equations with a linear strain