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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.