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A wall-law approximation for Jeffery-Hamel flows in rough wedges

  • Zijin Li
  • Xinghong Pan
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Abstract

We study the two-dimensional stationary Navier-Stokes equations in an unbounded wedge with small rough perturbations of its angular boundaries. The Jeffery-Hamel flow in the corresponding straight wedge is taken as the effective background flow. Under a suitable small-flux condition, we prove the existence of weak solutions and establish an H1-type energy error estimate of order O(ε2). For sufficiently small wedge angles, we further derive weighted estimates and improve the squared L2-error to O(ε3).

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Cite

BibTeXRIS
BibTeX
@misc{li2026walllaw,
  title = {{A wall-law approximation for Jeffery-Hamel flows in rough wedges}},
  author = {Zijin Li and Xinghong Pan},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.26736},
  eprint = {2608.26736},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.26736},
}
RIS
TY  - UNPB
TI  - A wall-law approximation for Jeffery-Hamel flows in rough wedges
AU  - Zijin Li
AU  - Xinghong Pan
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.26736
UR  - https://arxiv.org/abs/2608.26736
AB  - We study the two-dimensional stationary Navier-Stokes equations in an unbounded wedge with small rough perturbations of its angular boundaries. The Jeffery-Hamel flow in the corresponding straight wedge is taken as the effective background flow. Under a suitable small-flux condition, we prove the existence of weak solutions and establish an H^1-type energy error estimate of order O(ε^2). For sufficiently small wedge angles, we further derive weighted estimates and improve the squared L^2-error to O(ε^3).
ER  -