On the asymptotic behavior of solutions to the steady Navier-Stokes system in two-dimensional channels

Abstract: In this paper, we investigate the incompressible steady Navier-Stokes system with no-slip boundary condition in a two-dimensional channel. Given any flux, the existence of solutions is proved as long as the width of cross-section of the channel grows more slowly than the linear growth. Furthermore, if the flux is suitably small, the solution is unique even when the width of the channel is unbounded. Finally, based on the estimate of Dirichlet norm on the truncated domain, one could obtain the pointwise decay rate of the solution for arbitrary flux.