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Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle

Tom 70 / 2005

Reinhard Farwig Banach Center Publications 70 (2005), 73-84 MSC: 35C15, 35Q35, 76D05, 76D99, 76U05. DOI: 10.4064/bc70-0-5

Streszczenie

Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space $\mathbb R^3$. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper {Far} the author proved $L^q$-estimates of second order derivatives uniformly in the angular and translational velocities, $\omega$ and $k$, of the obstacle, whereas the transport terms fails to have $L^q$-estimates independent of $\omega$. In this paper we clarify this unexpected behavior and prove weighted $L^q$-estimates of first order terms independent of $\omega$.

Autorzy

  • Reinhard FarwigFachbereich Mathematik
    Darmstadt University of Technology
    D-64283 Darmstadt, Germany
    e-mail

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