Uniform structural stability and uniqueness of Poiseuille flows in a two dimensional periodic strip

2020/11/15 by Kaijian Sha, Yun Wang, Sha, Kaijian +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2011.07467

openalex publication_date 2020/11/15 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the uniform nonlinear structural stability of Poiseuille flows with arbitrarily large flux for the Navier-Stokes system in a two dimensional periodic strip when the period is not large. The key point is to establish the a priori estimate for the associated linearized problem via the careful analysis for the associated boundary layers. Furthermore, the well-posedness theory for the Navier-Stokes system is also proved even when the external force is large in L². Finally, if the vertical velocity is suitably small where the smallness is independent of the flux, then Poiseuille flow is the unique solution of the steady Navier-Stokes system in the periodic strip.

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• Uniqueness and uniform structural stability of Poiseuille flows in an infinitely long pipe with Navier boundary conditions

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