The essential spectrum of advective equations
Mathematical Physics
2009-11-10 v2 math.MP
Spectral Theory
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.
Cite
@article{arxiv.math-ph/0412019,
title = {The essential spectrum of advective equations},
author = {Roman Shvydkoy},
journal= {arXiv preprint arXiv:math-ph/0412019},
year = {2009}
}
Comments
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"