Stokes and Navier-Stokes equations with Navier boundary conditions

Abstract We study the stationary Stokes and Navier-Stokes equations with nonhomogeneous Navier boundary conditions in a bounded domain Ω ⊂ R 3 of class C 1 , 1 . We prove the existence and uniqueness of weak and strong solutions in W 1 , p ( Ω ) and W 2 , 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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