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\(L_{p}-L_{q}\) estimate of the Stokes operator and Navier-Stokes flows in the exterior of a rotating obstacle. (English) Zbl 1169.76015
Summary: We consider the motion of a viscous fluid filling the whole three-dimensional space exterior to a rotating obstacle with constant angular velocity. We develop the \(L_{p}-L_{q}\) estimates and the similar estimates in the Lorentz spaces of the Stokes semigroup with rotation effect. We next apply them to the Navier-Stokes equations to prove the global existence of a unique solution which goes to a stationary flow as \(t \rightarrow \infty \) with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in \(L_{3,\infty}\) (weak-\(L_{3}\) space).

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q30 Navier-Stokes equations
76U05 General theory of rotating fluids
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