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Exponential decay of the vorticity in the steady-state flow of a viscous liquid past a rotating body. (English) Zbl 1342.35244
Summary: Consider the flow of a Navier-Stokes liquid past a body rotating with a prescribed constant angular velocity, $$\omega$$, and assume that the motion is steady with respect to a body-fixed frame. In this paper we show that the vorticity field associated to every “weak” solution corresponding to data of arbitrary “size” (Leray Solution) must decay exponentially fast outside the wake region at sufficiently large distances from the body. Our result improves and generalizes in a non-trivial way famous results by D. C. Clark [Indiana Univ. Math. J. 20, 633–654 (1971; Zbl 0187.24506)] and K. I. Babenko and M. M. Vasil’ev [J. Appl. Math. Mech. 37, 651–665 (1973); translation from Prikl. Mat. Mekh. 37, 690–705 (1973; Zbl 0295.76015)] obtained in the case $$\omega=0$$.
##### MSC:
 35Q35 PDEs in connection with fluid mechanics 76U05 General theory of rotating fluids 76D05 Navier-Stokes equations for incompressible viscous fluids
##### Keywords:
rotating body; Navier-Stokes
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##### References:
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