Functional Analysis and Applications Seminar 

15/07/2004, 16:00 — 17:00 — Room P3.10, Mathematics Building
Reinhard Farwig, Darmstadt University of Technology, Germany

$L_q$-Analysis of Viscous Fluid Flow Past or Around a Rotating Obstacle

Consider the problem of time-periodic solutions of the Stokes and Navier-Stokes system modelling viscous incompressible fluid flow past or around a rotating three-dimensional obstacle. 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. This system admits a more or less explicit solution for the 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 we will use tools from harmonic analysis and a special maximal operator reflecting paths of fluid particles past or around the obstacle.