Boundedness and Stability of Solutions to the Non-autonomous Oseen-Navier-Stokes Equation

"We consider the motion of a viscous imcompressible fluid past rotating rigid body in three-dimensional, where translational and angular velocities are prescribed but time-dependent. In reference frame attached to body, we have non-autonomous Oseen-Navier-Stokes equations fixed exterior domains. We prove existence stability bounded mild solutions time t ONSE three-dimensional domains when coefficients dependent. Our method is based on L^p-L^q-estimates evolution family (U(t,s))¬¬ that its gradient boundedness solution linearized equations. After, use fixed-point arguments obtain result non-linearized data belong L^p-space sufficiently small. Finally, polynomial with same condition. useful for study time-periodic an "