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Asymptotic behavior of a Leray solution around a rotating obstacle. (English) Zbl 1247.35168
Escher, Joachim (ed.) et al., Parabolic problems. The Herbert Amann Festschrift. Based on the conference on nonlinear parabolic problems held in celebration of Herbert Amann’s 70th birthday at the Banach Center in Bȩdlewo, Poland, May 10–16, 2009. Basel: Birkhäuser (ISBN 978-3-0348-0074-7/hbk; 978-3-0348-0075-4/ebook). Progress in Nonlinear Differential Equations and Their Applications 80, 251-266 (2011).
Summary: We consider a body, \(\mathfrak B\), that rotates, without translating, in a Navier-Stokes liquid that fills the whole space exterior to \(\mathfrak B\). We analyze asymptotic properties of steady-state motions, that is, time-independent solutions to the equation of motion written in a frame attached to the body. We prove that “weak” steady-state solutions in the sense of J. Leray [J. Math. Pures Appl., IX. Sér. 12, 1–82 (1933; Zbl 0006.16702)] that satisfy the energy inequality are physically reasonable in the sense of R. Finn [Arch. Ration. Mech. Anal. 19, 363–406 (1965; Zbl 0149.44606)], provided the “size” of the data is suitably restricted.
For the entire collection see [Zbl 1220.35003].

MSC:
35Q74 PDEs in connection with mechanics of deformable solids
35Q30 Navier-Stokes equations
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids
35B40 Asymptotic behavior of solutions to PDEs
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