an:06587968
Zbl 1342.35244
Deuring, Paul; Galdi, Giovanni P.
Exponential decay of the vorticity in the steady-state flow of a viscous liquid past a rotating body
EN
Arch. Ration. Mech. Anal. 221, No. 1, 183-213 (2016).
00354577
2016
j
35Q35 76U05 76D05
rotating body; Navier-Stokes
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'' (\textit{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 \textit{D. C. Clark} [Indiana Univ. Math. J. 20, 633--654 (1971; Zbl 0187.24506)] and \textit{K. I. Babenko} and \textit{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 \(\omega=0\).
Zbl 0187.24506; Zbl 0295.76015