Three-Dimensional Stability of Burgers Vortices: the Low Reynolds Number Case

In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change in the circulation number (which characterizes the limiting vortex completely.) Our result is not restricted to the axisymmetric Burgers vortices, which have a simple analytic expression, but it applies to the whole family of non-axisymmetric vortices which are produced by a general uniaxial strain.