Mathematical analysis of an incompressible viscous fluid in an infinite layer by methods of real analysis

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We analyze a resolvent problem of the Stokes equation in an infinite layer and prove that the Stokes operator generates an analytic semigroup on Holder and Besov spaces. As an application, we prove a stability of some special solutions in Besov spaces. Moreover, we prove maximal regularity for the Stokes equation by operator-valued Fourier multiplier theorem, and we prove unique existence of a local in time solution to free boundary problems of the Navier-Stokes equation.