Article ID Journal Published Year Pages File Type
4592178 Journal of Functional Analysis 2009 20 Pages PDF
Abstract

In this paper we give a complete description of the Fredholm spectrum of the linearized 3D Euler equation in terms of the dynamical spectrum of the cocycle governing the evolution of shortwave perturbations. The argument is based on the pseudo differential representation of the Euler group and an application of an abstract isomorphism theorem for operator C∗-algebras. We further show that for all but countably many times the Fredholm spectrum of the group is rotationally invariant, and thus may consist of one or two concentric annuli. The results are obtained for a variety of other equations of ideal hydrodynamics.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory