L_p-L_q Estimate of the Stokes Operator and Navier鈥揝tokes Flows in the Exterior of a Rotating Obstacle

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• 作者：Toshiaki Hishida and Yoshihiro Shibata
• 刊名：Archive for Rational Mechanics and Analysis
• 出版时间：August, 2009
• 出版年：2009
• 期刊代码：15_0003-9527
• 类别：cp
• 卷：193
• 期：2
• 页码：339-421
• 数据来源：sp

摘要

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 equation to prove the global existence of a unique solution which goes to a stationary flow as t → ∞ with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in L _3,∞ (weak-L ₃ space).