On strong solutions of the Stokes equations in exterior domains

Abstract

We construct strong solutionsu, p/of the general nonhomogeneous Stokes equations -δu + ▽p=f inG, ▽ ·u=g inG, u=Φ on γ in an exterior domainG ⊂ℝn (n⩾3) with boundary γ of class C2. Our approach uses a localization technique: With the help of suitable cut-off functions and the solution of the divergence equation ▽ ·Ν=g inG, Ν = 0 on γ, the exterior domain problem is reduced to the entire space problem and an interior problem.