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.
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Luka Grubišić, Vadim Kostrykin, Konstantin A. Makarov, Stephan Schmitz, Krešimir Veselić, The Tan Theorem in fluid dynamics. J. Spectr. Theory 9 (2019), no. 4, pp. 1431–1457DOI 10.4171/JST/282