A weighted  L   q  ‐approach to Oseen flow around a rotating body | Zendy

Farwig R. | Zendy; Krbec M. | Zendy; Nečasová Š. | Zendy

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A weighted L q ‐approach to Oseen flow around a rotating body

Author(s) -

Farwig R.,

Krbec M.,

Nečasová Š.

Publication year - 2007

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.925

Subject(s) - mathematics , factorization , flow (mathematics) , univariate , mathematical analysis , a priori and a posteriori , pure mathematics , geometry , algorithm , philosophy , statistics , epistemology , multivariate statistics

We study time‐periodic Oseen flows past a rotating body in ℝ 3 proving weighted a priori estimates in L q ‐spaces using Muckenhoupt weights. After a time‐dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional terms (ω ∧ x ) ⋅ ∇ u and −ω ∧ u in the equation of momentum where ω 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. Copyright © 2007 John Wiley & Sons, Ltd.

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