An $L^q$-Analysis of Viscous Fluid Flow Past a Rotating Obstacle

Consider the problem of time-periodic strong solutions of the Stokes and Navier-Stokes system modelling viscous incompressible fluid flow past or around a rotating obstacle in $\mathbb{R}^3$. Introducing a rotating coordinate system attached to the body a linearization yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In this paper we find an explicit solution for the linear whole space problem when the axis of rotation is parallel to the velocity of the fluid at infinity. For the analysis of this solution in $L^q$-spaces, $1\lt q\lt \infty$, we will use tools from harmonic analysis and a special maximal operator reflecting paths of fluid particles past or around the obstacle.