2023/04/22 by Giuseppe Mulone, Mulone, Giuseppe
Engineering · Mathematics · #76E05 #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2304.12323
openalex publication_date 2023/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.