Uniqueness and uniform structural stability of Poiseuille flows in a periodic pipe with Navier boundary conditions

Abstract

In this paper, we prove the uniqueness and structural stability of Poiseuille flows for axisymmetric solutions of steady Navier-Stokes system supplemented with Navier boundary conditions in a periodic pipe. Moreover, the stability is uniform with respect to both the flux and the slip coefficient of Navier boundary conditions. It is also showed that the non-zero frequency part of the velocity is bounded by a power function of the flux with negative power as long as the flux is suitably large. One of the key ingredients of the analysis is to prove the uniform linear structural stability, where the analysis for the boundary layers and the swirl velocity corresponding to the flux and the slip coefficients in different regimes plays a crucial role.

arXiv commentarXiv admin note: text overlap with arXiv:1911.00749

References in corpus (4)

• Molecular scale contact line hydrodynamics of immiscible flows
• Transition threshold for the 3D Couette flow in Sobolev space
• Existence and asymptotic behavior of large axisymmetric solutions for steady Navier-Stokes system in a pipe
• Uniform structural stability and uniqueness of Poiseuille flows in a two dimensional periodic strip

Cited by in corpus (1)

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