3/8/2005

Roman Shvydkoy
University of Illinois at Chicago

The essential spectrum of advective equations

Early numerical simulations of certain 2D fluids revealed an important role of essential spectrum in formation of shortwave instabilities. For any linearized advective equation, such as the Euler equation, a general description of its essential spectrum can be given via the Sacker-Sell dynamical spectrum of an associated finite-dimensional system of ODEs. In this talk we discuss the relevant mathematical apparatus, and report on recent progress in finding the exact spectral pictures.