$ L^p $-Theory of the Stokes equation in a half space

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Stokes Resolvent Estimates in Spaces of Bounded Functions (2012, background): “= Rn. When Ω = Rn +, the analyticityof the semigroup is known in L∞-type spaces includingC 0,σ(Ω), the L∞-closure ofC∞ c,σ(Ω), the space of all smooth solenoidal vector ﬁelds compactly supported in Ω [12](see also [39], [28]). Their approach is based on explicit calculations of the solution operator”
New thoughts on old results of R.T. Seeley (2004, background): “Let us mention here too, that via the perturbation theorem, one obtains a new result on the H ∞ -calculus for the Stokes operator; see [NS02] for domains and [ DHP01a ] for the half-space.”