Abstract We consider the evolutionary Stokes system, coupled with the so-called dynamic slip boundary condition, in the simple geometry of a d -dimensional half-space. Using the standard technique of Fourier transform in tangential directions, we obtain an explicit formula for the resolvent. We then deduce estimates for both the weak (i. e. W^1, p W 1, p) and strong (hence W^2, p W 2, p) solutions, which are optimal in terms of the data belonging to an appropriate negative Sobolev or fractional Besov space. In the latter case Lᵖ L p -integrability of the pressure gradient is included. We allow for solutions with non-zero divergence, thus preparing the way for extensions to general domains. As a by-product, we show that the system generates an analytic semigroup in Lᵖ () 1. 111pt 1. 111ptLᵖ () L p (Ω) × L p (∂ Ω). Our approach remains elementary in the sense that only the classical Mikhlin multiplier theorem will be used. The methods of H^ H ∞ -calculus are implicitly present; but we stay away from the concept of R -boundedness and related heavy functional analytic machinery.
Pražák et al. (Mon,) studied this question.