Speaker: Gene Wayne
Title: Stability of Burgers' Vortices in the Three-dimensional
Navier-Stokes equations
Abstract: I will describe joint work with Th. Gallay of the Univ. of
Grenoble in which we prove the existence of non-axisymmetric
analogues of the Burgers vortex solution of the Navier-Stokes
equation. These solutions exist for arbitrarily large values
of the Reynolds number. In addition we show that for small
Reynolds number these solutions are stable. More precisely,
we prove that any solution of the three-dimensional Navier-Stokes equations
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.)
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