On the Navier-Stokes equations with rotating effect and prescribed outflow velocity

Details On the Navier-Stokes equations with rotating effect and prescribed outflow velocity On the Navier-Stokes equations with rotating effect and prescribed outflow velocity

2009-05-09

arxiv.org/abs/0905.1397v4

Mathematics

Analysis of PDEs

18 pages, to appear in J. Math. Fluid Mech. (published online first)

Scientific paper

10.1007/s00021-010-0026-x

We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\R^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the prescribed velocity vector is assumed to be parallel to the axis of rotation, in this paper we are interested in a general outflow velocity. In order to use $L^p$-techniques we introduce a new coordinate system, in which we obtain a non-autonomous partial differential equation with an unbounded drift term. We prove that the linearized problem in $\R^d$ is solved by an evolution system on $L^p_{\sigma}(\mathbb R^d)$ for $1

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