The Tan 2Θ2 \Theta Theorem in fluid dynamics

  • Luka Grubišić

    University of Zagreb, Croatia
  • Vadim Kostrykin

    Johannes Gutenberg-Universität Mainz, Germany
  • Konstantin A. Makarov

    University of Missouri, Columbia, USA
  • Stephan Schmitz

    Universität Koblenz-Landau, Germany
  • Krešimir Veselić

    Fernuniversität Hagen, Germany
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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 this article

Luka Grubišić, Vadim Kostrykin, Konstantin A. Makarov, Stephan Schmitz, Krešimir Veselić, The Tan 2Θ2 \Theta Theorem in fluid dynamics. J. Spectr. Theory 9 (2019), no. 4, pp. 1431–1457

DOI 10.4171/JST/282