33 research outputs found
Maximal regularity of the time-periodic Navier-Stokes system
Time-periodic solutions to the linearized Navier-Stokes system in the
-dimensional whole-space are investigated. For time-periodic data in
-spaces, maximal regularity and corresponding a priori estimates for the
associated time-periodic solutions are established. More specifically, a Banach
space of time-periodic vector fields is identified with the property that the
linearized Navier-Stokes operator maps this space homeomorphically onto the
-space of time-periodic data.Comment: 19 page
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Viscous Flow Around a Rigid Body Performing a Time-periodic Motion
The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces