Squire's theorem for nonlinear monotone energy stability

Abstract

The Squire's theorem holds for parallel shear flows governed by the linearized Navier-Stokes equations. 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 \cite[p. 627]{Squire1933}. Instead, for nonlinear Navier-Stokes system it is supposed that the theorem does not hold in general (see Drazin and Reid \cite[pp. 429--430]{DrazinReid2004}). Here we prove that the Squire theorem holds also for nonlinear monotone energy stability of parallel shear flows that include Couette and Poiseuille flows between parallel walls.

arXiv comment7 pages. arXiv admin note: substantial text overlap with arXiv:2304.11416; text overlap with arXiv:2304.11545