The Stationary Navier-stokes System in Nonsmooth Manifolds: the Poisson Problem in Lipschitz and C Domains
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چکیده
In this paper we study the linearized version of the stationary Navier-Stokes equations on a fixed subdomain Ω of a smooth, compact Riemannian manifold M . Let Tr denote the trace on ∂Ω. With Def standing for the deformation tensor and with d denoting the exterior derivative operator on M , set L = 2 Def∗Def, δ = d∗. We consider the Dirichlet problem for the (modified) Stokes system Lu+∇ωu+ dπ = f ∈ Lps+ 1 p −2(Ω,Λ TM), δu = h ∈ L s+ 1 p −1(Ω), Tru = g ∈ B s (∂Ω,ΛTM). (1.1)
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