Abstract

We study the stationary Stokes and Navier-Stokes equations with nonhomogeneous Navier boundary conditions in a bounded domain Ω⊂R3 of class C1,1. We prove the existence and uniqueness of weak and strong solutions in W1,p(Ω) and W2,p(Ω) for all 1<p<∞, considering minimal regularity on the friction coefficient α. Moreover, we deduce uniform estimates for the solution with respect to α which enables us to analyze the behavior of the solution when α→∞.

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