Klaus Widmayer, École polytechnique fédérale de Lausanne
Please note that this seminar will take place online via Zoom. You can connect to this seminar via the following link:
Abstract: We review some recent results on the asymptotic stability of stationary solutions to the two-dimensional Euler and Navier-Stokes equations of incompressible flow. In many cases, nonlinear asymptotic stability of certain stationary solutions follows by way of decay mechanisms in the associated linearized problems -- both in the Euler equations (through so-called inviscid damping) and in the Navier-Stokes equations (via enhanced dissipation).
In contrast, we will see that the dynamics near the so-called Kolmogorov flow are more complex: in particular, while linear stability holds, nonlinear asymptotic stability is false, even for analytic perturbations.
This is joint work with Michele Coti Zelati and Tarek Elgindi.