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Weighted $L^{2}$ and $L^{q}$ approaches to fluid flow past a rotating body

Tom 86 / 2009

R. Farwig, S. Kračmar, M. Krbec, Š. Nečasová, P. Penel Banach Center Publications 86 (2009), 59-81 MSC: Primary 76D05; Secondary 35Q30, 35Q35. DOI: 10.4064/bc86-0-4

Streszczenie

Consider the flow of a viscous, incompressible fluid past a rotating obstacle with velocity at infinity parallel to the axis of rotation. After a coordinate transform in order to reduce the problem to a Navier-Stokes system on a fixed exterior domain and a subsequent linearization we are led to a modified Oseen system with two additional terms one of which is not subordinate to the Laplacean. In this paper we describe two different approaches to this problem in the whole space case. One of them is based on a variational method in $L^2$-spaces with weights reflecting the anisotropic behaviour of the Oseen fundamental solution. The other approach uses weighted multiplier theory, interpolation and Littlewood-Paley theory to get a priori estimates in anisotropically weighted $L^q$-spaces.

Autorzy

  • R. FarwigDepartment of Mathematics
    Darmstadt University of Technology
    64289 Darmstadt, Germany
    e-mail
  • S. KračmarDepartment of Technical Mathematics
    Czech Technical University
    Karlovo nám. 13
    121 35 Prague 2, Czech Republic
    e-mail
  • M. KrbecInstitute of Mathematics
    Academy of Sciences of the Czech Republic
    Žitná 25
    11567 Prague 1, Czech Republic
    e-mail
  • Š. NečasováInstitute of Mathematics
    Academy of Sciences of the Czech Republic
    Žitná 25
    11567 Prague 1, Czech Republic
    e-mail
  • P. PenelUniversité du Sud Toulon-Var
    Mathématiques
    B.P. 20132
    83957 La Garde Cedex, France
    e-mail

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