# Uniform Structural stability of Hagen-Poiseuille flows in a pipe

@article{Wang2019UniformSS, title={Uniform Structural stability of Hagen-Poiseuille flows in a pipe}, author={Yun Wang and Chunjing Xie}, journal={arXiv: Analysis of PDEs}, year={2019} }

In this paper, we prove the uniform nonlinear structural stability of Hagen-Poiseuille flows with arbitrary large fluxes in the axisymmetric case. This uniform nonlinear structural stability is the first step to study Liouville type theorem for steady solution of Navier-Stokes system in a pipe, which may play an important role in proving the existence of solutions for the Leray's problem, the existence of solutions of steady Navier-Stokes system with arbitrary flux in a general nozzle. A key…

## 5 Citations

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

- Mathematics
- 2021

In this paper, uniqueness and uniform structural stability of Poiseuille flows in an infinitely long pipe with Navier boundary conditions are established for axisymmetric solutions of steady…

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

- Mathematics
- 2021

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…

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

- Physics, Mathematics
- 2020

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…

Existence and asymptotic behavior of large axisymmetric solutions for steady Navier-Stokes system in a pipe

- Physics, Mathematics
- 2020

In this paper, the existence and uniqueness of strong axisymmetric solutions with large flux for the steady Navier-Stokes system in a pipe are established even when the external force is also…

Characterization of bounded smooth solutions to the axially symmetric Navier-Stokes equations in an infinite pipe with Navier-slip boundary

- Mathematics
- 2021

Bounded smooth solutions of the stationary axially symmetric Navier-Stokes equations in an infinite pipe, equipped with the Navier-slip boundary condition, are considered in this paper. Here “smooth”…

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