Applied Mathematics Colloquium: Dr. Edriss S. Titi

Title: Is dispersion a stabilizing or destabilizing mechanism?   Landau damping in fast oscillating turbulent flows

In this talk I will present a unified approach for the effect of fast rotation and dispersion as an averaging mechanism for, on the one hand, regularizing and stabilizing certain evolution equations, such as the Navier–Stokes and Burgers' equations.  On the other hand, I will also present some results in which large dispersion acts as a destabilizing mechanism for the long-time dynamics of certain dissipative evolution equations, such as the Kuramoto–Sivashinsky equation.

In addition, I will present some new results concerning two- and three-dimensional turbulent flows with high Reynolds numbers in periodic domains, which exhibit Landau damping mechanism due to large spatial average in the initial data.