Is dispersion a stabilizing or destabilizing mechanism? Landau-damping induced by fast background ows

Edriss Titi , University of Cambridge 2.28.0.10810:15 - 11:45

In this talk, I will present a unifed approach for the effect of fast rotation and dispersion as an averaging mechanism for 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 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.