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A weighted Lq-approach to Oseen flow around a rotating body

✍ Scribed by R. Farwig; M. Krbec; Š. Nečasová

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
221 KB
Volume
31
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

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.

📜 SIMILAR VOLUMES

Strong solutions to the Stokes equations
Strong solutions to the Stokes equations of a flow around a rotating body in weighted Lq spaces
✍ Šárka Nečasová; Katrin Schumacher 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 176 KB 👁 1 views

We consider the motion of a fluid in the exterior of a rotating obstacle. This leads to a modified version of the Stokes system which we consider in the whole space R n , n = 2 or n = 3 and in an exterior domain D ⊂ R 3 . For every q ∈ (1, ∞) we prove existence of solutions and estimates in function