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A weighted \(L^q\)-approach to Stokes flow around a rotating body. (English) Zbl 1248.35158
Summary: Considering time-periodic Stokes flow around a rotating body in \({\mathbb R^2}\) or \({\mathbb R^3}\) we prove weighted a priori estimates in \(L^q\)-spaces for the whole space problem. After a time-dependent change of coordinates the problem is reduced to a stationary Stokes equation with the additional term \({(\omega \times x)\cdot\nabla u}\) in the equation of momentum, where \(\omega \) denotes the angular velocity. In cylindrical coordinates attached to the rotating body we allow for Muckenhoupt weights which may be anisotropic or even depend on the angular variable and prove weighted \(L^q\)-estimates using the weighted theory of Littlewood-Paley decomposition and of maximal operators.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B45 A priori estimates in context of PDEs
46N20 Applications of functional analysis to differential and integral equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
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