Navier-Stokes equations on Lipschitz domains in Riemannian manifolds

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The Incompressible Navier–Stokes Equations on Non-compact Manifolds (2014, background): “of a Laplacian on vector ﬁelds on Riemannian manifolds: there are at least two candidates for the role of Laplace operator, i.e. the Bochner and Hodge Laplacians. Following [17], [54] (see also [50], [43]), the correct formulation is obtained by introducing the stress tensor. Let us recall that on R”
Differential operators and boundary value problems on hypersurfaces (2006, methodology): “Once again, this follows by translating the main result in [ MT2 ] by means of the identifications (6.3).”
The Stationary Navier-Stokes System in Nonsmooth Manifolds: The Poisson Problem in Lipschitz and C1 Domains (2004, methodology): “10) of [45], LΦ− I = Pd(LΦ− I) thus, by adjunction, ΦL− I = (ΦL− I)Pd = (ΦL− I)dδG = (ΦL− I)dG0δ.”
The regularity of the Stokes operator and the Fujita–Kato approach to the Navier–Stokes initial value problem in Lipschitz domains (2008, methodology): “First, central to our approach to the regularity of the Stokes operator are the well-posedness results for the homogeneous and inhomogeneous Dirichlet problems for the Stokes system in Lipschitz domains from [17] and [41].”