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A weighted \(L^q\)-approach to Oseen flow around a rotating body. (English) Zbl 1132.76015
Summary: We study time-periodic Oseen flows past a rotating body in \(\mathbb R^3\) proving weighted a priori estimates in \(L^q\)-spaces using Muckenhoupt weights. After a time-dependant change of coordinates, the problem is reduced to a stationary Oseen equation with additional terms \((w \wedge x) \cdot \nabla u \) and \(-\omega \wedge u\) in the momentum equation, where \(\omega \) denotes the angular velocity. Due to the asymmetry of Oseen flow and to describe its wake, we use anisotropic Muckenhoupt weights, a weighted theory of Littlewood-Paley decomposition and of maximal operators as well as one-sided univariate weights, one-sided maximal operators and a new version of Jones’ factorization theorem.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids
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