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On a resolvent estimate of the Stokes equation on an infinite layer. (English) Zbl 1048.35052
The authors establish the weak solvability of the title problem, and prove standard $$L_p$$ estimates for the solution. The proof is based on a partial Fourier transform which reduces the original problem to a two-point boundary value problem for a system of ordinary differential equations with parameter. Then an application of Agmon-Douglis-Nirenberg type estimates of singular integrals provides the desired result.

##### MSC:
 35Q30 Navier-Stokes equations 76D07 Stokes and related (Oseen, etc.) flows
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