Weighted $L^{2}$ and $L^{q}$ approaches to fluid flow past a rotating body
Volume 86 / 2009
Abstract
Consider the flow of a viscous, incompressible fluid past a rotating obstacle with velocity at infinity parallel to the axis of rotation. After a coordinate transform in order to reduce the problem to a Navier-Stokes system on a fixed exterior domain and a subsequent linearization we are led to a modified Oseen system with two additional terms one of which is not subordinate to the Laplacean. In this paper we describe two different approaches to this problem in the whole space case. One of them is based on a variational method in $L^2$-spaces with weights reflecting the anisotropic behaviour of the Oseen fundamental solution. The other approach uses weighted multiplier theory, interpolation and Littlewood-Paley theory to get a priori estimates in anisotropically weighted $L^q$-spaces.
