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.Comment: 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 Ma\~{n}e sequences with an application to ideal fluids