Lp-Lq Estimate of the Stokes Operator and Navier–Stokes Flows in the Exterior of a Rotating Obstacle
Lp-Lq Estimate of the Stokes Operator and Navier–Stokes Flows in the Exterior of a Rotating Obstacle
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DOI：
10.1007/s00205-008-0130-8
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发表时间：
2009-08
影响因子：
2.5
通讯作者：
T. Hishida;Y. Shibata
中科院分区：
文献类型：
--
作者：
T. Hishida;Y. Shibata
本文考虑了在具有常角速度的旋转障碍物外，充满整个三维空间的粘性流体的运动。本文在具有旋转效应的Stokes半群的Lorentz空间中建立了Lp-Lq估计和类似的估计。然后将它们应用于Navier-Stokes方程，证明了在L3，∞（弱L3空间）中，当定常流和初始扰动都足够小时，以一定速率到达定常流ast→ ∞的唯一解的整体存在性.
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 theLp-Lqestimates and the similar estimates in the Lorentz spaces of the Stokes semigroup with rotation effect. We next apply them to the Navier–Stokes equation to prove the global existence of a unique solution which goes to a stationary flow ast→ ∞ with some definite rates when both the stationary flow and the initial disturbance are sufficiently small inL3,∞(weak-L3space).