ANNALI DELL'UNIVERSITA' DI FERRARA

, 54:61

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

  • Reinhard Farwig
  • Miroslav Krbec
  • Šárka Nečasová
Article

DOI: 10.1007/s11565-008-0040-6

Cite this article as:
Farwig, R., Krbec, M. & Nečasová, Š. Ann. Univ. Ferrara (2008) 54: 61. doi:10.1007/s11565-008-0040-6

Abstract

Considering time-periodic Stokes flow around a rotating body in \({\mathbb R^2}\) or \({\mathbb R^3}\) we prove weighted a priori estimates in Lq-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 ω 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 Lq-estimates using the weighted theory of Littlewood-Paley decomposition and of maximal operators.

Keywords

Littlewood-Paley theoryMaximal operatorsRotating obstaclesStationary Stokes flowWeighted estimatesComplex interpolation

Mathematics Subject Classification (2000)

76D0535Q3042B2546E35

Copyright information

© Università degli Studi di Ferrara 2008

Authors and Affiliations

  • Reinhard Farwig
    • 1
  • Miroslav Krbec
    • 2
  • Šárka Nečasová
    • 2
  1. 1.Department of MathematicsDarmstadt University of TechnologyDarmstadtGermany
  2. 2.Mathematical Institute of Academy of SciencesPrague 1Czech Republic