Pointwise decay of steady Navier--Stokes flows with Navier-slip boundary condition in two-dimensional channels
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Han, Han, Jingwen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223158261