On a resolvent estimate of the Stokes equation on an infinite layer

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The stokes equation in the Lp-setting: Well-posedness and regularity properties (2018, background): “/ was proved by Abe and Shibata in [6, 7] and by Abels and Wiegner in [15].”
The L∞-Stokes semigroup in exterior domains (2012, unknown): “In order to approximate solutions in a uniformly regular domain, we appeal to L̃r theory [13,15], although Lr -theory works for more general domains [3,16,17,20].”
Analyticity of the Stokes semigroup in spaces of bounded functions (2011, unknown): “Although there are several results on analyticity of S(t) in Lσ for various domains such as a half space, a bounded domain [26], [52], an exterior domain [10], [34], an aperture domain [18], a layer domain [1], a perturbed half space [17] (even for variable viscosity coefficients) [3], [2], the resu”
Stokes Resolvent Estimates in Spaces of Bounded Functions (2012, background): “By now, analyticity results are known for other type unbounded domains, see [17, 18], [4] ([6, 5] with variable viscosity coefficients) and Lipschitz domains [33].”