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The Stokes equations in layer domains on spaces of bounded and integrable functions

The Stokes equations in a layer domain are investigated. For the case of a two‐dimensional layer it is shown by resolvent estimates that there exists a semigroup of angle π/2 on solenoidal subspaces of L∞ and L1. Furthermore, the stationary problem for dimension two is solvable in these spaces. It is also shown that both results cannot be extended to three and higher dimensions in the same setting.