An \(L^q\)-analysis of viscous fluid flow past a rotating obstacle. (English) Zbl 1136.76340

Farwig, Reinhard

Tohoku Math. J. (2) 58, No. 1, 129-147 (2006).

Summary: 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, \(1<q<\infty\), we will use tools from harmonic analysis and a special maximal operator reflecting paths of fluid particles past or around the obstacle.

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
35C15	Integral representations of solutions to PDEs
35Q35	PDEs in connection with fluid mechanics
76D99	Incompressible viscous fluids
76U05	General theory of rotating fluids

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