Navier-Stokes equations in thin 3D domains with Navier boundary conditions

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The uniform Korn–Poincaré inequality in thin domains (2008, background): “Towards analysing thin domains other than simple product domains, Iftimie, Raugel and Sell [12] treated domains of the type: Ω = {x ∈ R3; (x1, x2) ∈ Q, 0 < x3 < g(x1, x2)}, with the mixed boundary conditions: periodic on the lateral boundary and the Navier boundary conditions: D(u) nh ‖ nh and u ·…”
Strong solutions to the Navier-Stokes equations on thin 3D domains (2012, background): “ On the other hand S. Montgomery-Smith ([10, Theorem 1]) improved the result from [9] Through the ﬁrst decade in the 21st century further improvements of the powers pi and qi were made (see e.g. [5], [6], [7], [8]). In [5] also weaker restriction on the data was imposed, namely A14 N ǫv0 was assumed”