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

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 shown that the nonzero 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 detailed analysis for the boundary layers and the swirl velocity corresponding to the flux and the slip coefficients in different regimes plays a crucial role.

Automated summary

In this paper, the uniqueness and structural stability of Poiseuille flows for axisymmetric solutions of steady Navier-Stokes system with Navier boundary conditions in a periodic pipe are proven. The stability is also shown to be uniform with respect to both the flux and the slip coefficient of Navier boundary conditions. Furthermore, it is demonstrated that the nonzero frequency part of the velocity is bounded by a negative power function of the flux as long as the flux is suitably large. The analysis highlights the importance of uniform linear structural stability and detailed analysis of boundary layers and swirl velocity corresponding to the flux and slip coefficients in different regimes.