Squire’s theorem for monotone energy stability of plane shear flows for Navier-Stokes-Voigt fluids with vertical throughflow

Abstract The Squire theorem holds for parallel shear flows governed by the linearized Navier-Stokes equations. In his paper Squire writes “For the study of the stability of flow between parallel walls it is sufficient to confine attention to disturbances of two-dimensional type”, Squire (Proc R Soc A 142:621, 1933). Conversely, for nonlinear Navier-Stokes system it is supposed that the Squire’s theorem does not hold in general (see Drazin and Reid Drazin in (Hydrodynamic Stability. Cambridge Mon