Work

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

Year: 2023

Type: article

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 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.

Source: Mathematical Models and Methods in Applied Sciences

DOI: 10.1142/s0218202523500070

Authors: Yun Wang, Chunjing Xie

Institutions: Soochow University, Shanghai Jiao Tong University

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Natural Science Foundation of Shanghai, National Natural Science Foundation of China, Program of Shanghai Academic Research Leader