Mathematics Colloquium
Edriss S. Titi
University of Cambridge and
Texas A&M University and
Weizmann Institute of Science
Title: Is dispersion a stabilizing or destabilizing
mechanism? Landau-damping induced by fast background flows
Date: Monday, March 23, 2020
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm
Abstract. 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 ``Landua-damping" mechanism due to large spatial average in the initial data.