The essential spectrum of advective equations

Abstract

A description of the essential spectrum is given for a general class of linear advective PDE with pseudodifferential bounded perturbation. We prove that every point in the Sacker-Sell spectrum of the corresponding bicharacteristic-amplitude system exponentiates into the spectrum of PDE. Exact spectral pictures are found in various cases. Applications to instability are presented.

This replaces the earlier version of the paper. The content of the original submission appeared in two publications -- this present one and the other one entitled "Cocycles and Mañe sequences with an application to ideal fluids"