Stokes and Navier-Stokes equations with Navier boundary conditions

We study the stationary Stokes and Navier-Stokes equations with nonhomogeneous Navier boundary conditions in a bounded domain Omega subset of R-3 of class C-1,C-1. We prove the existence and uniqueness of weak and strong solutions in W-1,W-p(Omega) and W-2,W-p(Omega) for all 1 < p < infinity, considering minimal regularity on the friction coefficient alpha. Moreover, we deduce uniform estimates for the solution with respect to alpha which enables us to analyze the behavior of the solution when alpha -> infinity. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study proves the existence and uniqueness of weak and strong solutions in W-1,W-p(Ω) and W-2,W-p(Ω) with minimal regularity on the friction coefficient α. Additionally, uniform estimates are deduced for the solution with respect to α, allowing for analysis of the solution's behavior as α approaches infinity.