Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

Abstract The equations governing the flow of a viscous incompressible fluid around rigid body that performs prescribed time-periodic motion with constant axes translation and rotation are investigated. Under assumption period angular velocity rigid-body compatible, mean translational is non-zero, existence solution established. proof based on an appropriate linearization, which examined within setting absolutely convergent Fourier series. Since corresponding resolvent problem ill-posed in classical Sobolev spaces, linear theory developed framework homogeneous spaces.