MR2381323 Reinhard FARWIG and Toshiaki HISHIDA Reinhard FARWIG and Toshiaki HISHIDA Stationary Navier-Stokes Flow Around a Rotating Obstacle Funkcialaj Ekvacioj. Serio Internacia 50 2007 371--403 http://fe.math.kobe-u.ac.jp/FE/FullPapers/50-3/50_371.pdf http://www.ams.org/mathscinet-getitem?mr=MR2381323 Consider a viscous incompressible fluid filling the whole 3-dimensional space exterior to a rotating body with constant angular velocity $\omega$. By using a coordinate system attached to the body, the problem is reduced to an equivalent one in a fixed exterior domain. The reduced equation involves the crucial drift operator $(\omega\wedge x)\cdot\nabla$, which is not subordinate to the usual Stokes operator. This paper addresses stationary flows to the reduced problem with an external force $f=\mbox{div} F$, that is, time-periodic flows to the original one. Generalizing previous results of G. P. Galdi [20] we show the existence of a unique solution $(\nabla u,p)$ in the class $L_{3/2,\infty}$ when both $F\in L_{3/2,\infty}$ and $\omega$ are small enough; here $L_{3/2,\infty}$ is the weak-$L_{3/2}$ space. Navier-Stokes flow, Rotating obstacle, Exterior domain, Weak stationary solutions, Weak-$L_p$ spaces. 35Q30, 76D05. 50-371 2007 Stationary Navier-Stokes Flow Around a Rotating Obstacle Reinhard FARWIG and Toshiaki HISHIDA Reinhard FARWIG and Toshiaki HISHIDA 1 Bergh, J.; Löfström, J. Interpolation Spaces Springer, Berlin 1976 MR0482275
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