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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.

Keywords

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"

R2 v1 2026-07-22T16:25:20.501Z