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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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Cite

BibTeXRIS
BibTeX
@misc{jia2026steady,
  title = {{Steady symmetric Navier-Stokes flow near Poiseuille flow: existence and vanishing viscosity limit}},
  author = {Zeyu Jia and Jia Song and Tao Tao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18280},
  eprint = {2609.18280},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18280},
}
RIS
TY  - UNPB
TI  - Steady symmetric Navier-Stokes flow near Poiseuille flow: existence and vanishing viscosity limit
AU  - Zeyu Jia
AU  - Jia Song
AU  - Tao Tao
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18280
UR  - https://arxiv.org/abs/2609.18280
AB  - 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.
ER  -