The Tan $2 \Theta$-Theorem in Fluid Dynamics
Spectral Theory
2020-01-07 v1 Functional Analysis
Abstract
We show that the generalized Reynolds number (in fluid dynamics) introduced by Ladyzhenskaya is closely related to the rotation of the positive spectral subspace of the Stokes block-operator in the underlying Hilbert space. We also explicitly evaluate the bottom of the negative spectrum of the Stokes operator and prove a sharp inequality relating the distance from the bottom of its spectrum to the origin and the length of the first positive gap.
Cite
@article{arxiv.1708.00509,
title = {The Tan $2 \Theta$-Theorem in Fluid Dynamics},
author = {Luka Grubišić and Vadim Kostrykin and Konstantin A. Makarov and Stephan Schmitz and Krešimir Veselić},
journal= {arXiv preprint arXiv:1708.00509},
year = {2020}
}
Comments
19 pages, 2 figures