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arXiv · 2609.18280

Steady symmetric Navier-Stokes flow near Poiseuille flow: existence and vanishing viscosity limit

Zeyu Jia·Jia Song·Tao Tao
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Abstract

We study the existence and vanishing viscosity limit of steady incompressible Navier-Stokes flows in a horizontally periodic strip with no slip boundary conditions and midline symmetric forcing. Taking a Poiseuille flow as the leading order Euler profile, we construct higher order symmetric approximate solutions and establish the existence of a symmetric solution to the associated nonlinear error equation. Under suitable compatibility conditions on the forcing, this construction yields a family of midline symmetric steady Navier-Stokes solutions that converges to the prescribed Poiseuille flow at the optimal rate.

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Zeyu Jia, Jia Song, Tao Tao. 2026-09-16. Steady symmetric Navier-Stokes flow near Poiseuille flow: existence and vanishing viscosity limit. https://arxiv.org/abs/2609.18280

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