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arXiv · 2610.27501

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 \[ |\Bu(x_1,x_2)|\le \frac{C}{f(x_1)}, \] 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.

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Han Li, Jingwen Han. 2026-10-20. Pointwise decay of steady Navier--Stokes flows with Navier-slip boundary condition in two-dimensional channels. https://arxiv.org/abs/2610.27501

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