Tohoku Mathematical Journal

An $L^{\lowercase{q}}$-analysis of viscous fluid flow past a rotating obstacle

Reinhard Farwig

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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 Euclidean three-space. 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, $1<q<\ue$, we will use tools from harmonic analysis and a special maximal operator reflecting paths of fluid particles past or around the obstacle.

Article information

Tohoku Math. J. (2), Volume 58, Number 1 (2006), 129-147.

First available in Project Euclid: 18 April 2006

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Zentralblatt MATH identifier

Primary: 76D05: Navier-Stokes equations [See also 35Q30]
Secondary: 35C15: Integral representations of solutions 35Q35: PDEs in connection with fluid mechanics 76D99: None of the above, but in this section 76U05: Rotating fluids

Littlewood-Paley theory maximal operators Oseen flow rotating obstacles singular integral operator Stokes flow


Farwig, Reinhard. An $L^{\lowercase{q}}$-analysis of viscous fluid flow past a rotating obstacle. Tohoku Math. J. (2) 58 (2006), no. 1, 129--147. doi:10.2748/tmj/1145390210.

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