Squire's theorem for nonlinear monotone energy stability
Mathematical Physics
2023-04-26 v1 math.MP
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.
Keywords
Cite
@article{arxiv.2304.12323,
title = {Squire's theorem for nonlinear monotone energy stability},
author = {Giuseppe Mulone},
journal= {arXiv preprint arXiv:2304.12323},
year = {2023}
}
Comments
7 pages. arXiv admin note: substantial text overlap with arXiv:2304.11416; text overlap with arXiv:2304.11545