The Tan $2\Theta$-Theorem in Fluid Dynamics

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.

19 pages, 2 figures

References in corpus (2)

• Angles Between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods
• Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators

Cited by in corpus (2)

• Maximal $L^p$-regularity and $H^{\infty }$-calculus for block operator matrices and applications
• On a minimax principle in spectral gaps