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arXiv · 2003.07026

On the $C_0$ semigroup generated by the Oseen operator around a steady flow exterior to a rotating obstacle

Jingyue Li·Changxing Miao·Xiaoxin Zheng
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Abstract

We consider the motion of an incompressible viscous fluid filling the whole space exterior to a moving with rotation and translation obstacle. We show that the Stokes operator around the steady flow in the exterior of this obstacle generates a $C_0$-semigroup in $L^p$ space and then develop a series of $L^p$-$L^q$ estimates of such semigroup. As an application, we give out the stability of such steady flow when the initial disturbance in $L^3$ and the steady flow are sufficiently small.

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Jingyue Li, Changxing Miao, Xiaoxin Zheng. 2020-03-16. On the $C_0$ semigroup generated by the Oseen operator around a steady flow exterior to a rotating obstacle. https://arxiv.org/abs/2003.07026

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