Strong Solutions to the Navier-Stokes Equations Around a Rotating Obstacle

We study the existence of strong solutions to the three-dimensional Navier-Stokes initial-boundary value problem in the domain, , exterior to a rigid body that rotates with constant angular velocity, . We show that when the initial data, u₀, are prescribed in an appropriate functional class, a strong solution exists at least in some finite time interval. Moreover, the solution exists for all times, provided u₀, in suitable norm, and the magnitude of do not exceed a certain constant depending only on the kinematic viscosity and on the regularity of . In this latter case, we also show that the velocity field converges to the velocity field of the corresponding steady-state solution.