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The Squire's theorem holds for parallel shear flows governed by thelinearized Navier-Stokes equations. Squire writes ``For the study of thestability of flow between parallel walls it is sufficient to confine attentionto disturbances of two-dimensional type", Squire \cite[p. 627]{Squire1933}.Instead, for nonlinear Navier-Stokes system it is supposed that the theoremdoes not hold in general (see Drazin and Reid \cite[pp.429--430]{DrazinReid2004}). Here we prove that the Squire theorem holds alsofor nonlinear monotone energy stability of parallel shear flows that includeCouette and Poiseuille flows between parallel walls.

Squire's theorem for nonlinear monotone energy stability