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Pointwise decay of steady Navier--Stokes flows with Navier-slip boundary condition in two-dimensional channels

  • Han Li
  • Jingwen Han
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Abstract

We establish a pointwise decay estimate for steady incompressible Navier--Stokes flows in two-dimensional channels with positive Navier friction coefficient. Specifically, for the arbitrary-flux solutions constructed by Sha, Wang, and Xie \cite{SWX22f}, under suitable outlet conditions and weighted geometric bounds on the channel walls, we show |Bu(x1,x2)|≤ C/f(x1), where f is the channel width. Our decay rate is optimal in the cross-sectional supremum norm when the prescribed flux is nonzero. The main difficulty is that rescaling by the local width changes the Navier friction coefficient into a potentially large parameter. The key technique is to establish a local Stokes boundary estimate uniform in this parameter.

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Cite

BibTeXRIS
BibTeX
@misc{li2026pointwise,
  title = {{Pointwise decay of steady Navier--Stokes flows with Navier-slip boundary condition in two-dimensional channels}},
  author = {Han Li and Jingwen Han},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27501},
  eprint = {2610.27501},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27501},
}
RIS
TY  - UNPB
TI  - Pointwise decay of steady Navier--Stokes flows with Navier-slip boundary condition in two-dimensional channels
AU  - Han Li
AU  - Jingwen Han
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27501
UR  - https://arxiv.org/abs/2610.27501
AB  - We establish a pointwise decay estimate for steady incompressible Navier--Stokes flows in two-dimensional channels with positive Navier friction coefficient. Specifically, for the arbitrary-flux solutions constructed by Sha, Wang, and Xie \cite{SWX22f}, under suitable outlet conditions and weighted geometric bounds on the channel walls, we show |Bu(x_1,x_2)|≤ C/f(x_1), where f is the channel width. Our decay rate is optimal in the cross-sectional supremum norm when the prescribed flux is nonzero. The main difficulty is that rescaling by the local width changes the Navier friction coefficient into a potentially large parameter. The key technique is to establish a local Stokes boundary estimate uniform in this parameter.
ER  -