On the C0 semigroup generated by the Oseen operator around a steady flow exterior to a rotating obstacle

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.