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The Tan 2Θ Theorem in fluid dynamics

2017

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.

Spectral subspacePhysics35Q35 47A67 (Primary) 35Q30 47A12 (Secondary)Spectrum (functional analysis)Mathematical analysisHilbert spaceReynolds numberStatistical and Nonlinear PhysicsMathematics - Spectral TheoryMathematics - Functional AnalysisPhysics::Fluid Dynamicssymbols.namesakeFluid dynamicssymbolsGeometry and TopologyStokes operatorNavier–Stokes equation ; Stokes operator ; Reynolds number ; rotation of subspaces ; quadratic forms ; quadratic numerical rangeRotation (mathematics)Mathematical Physics
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