The Cauchy problem for the Navier-Stokes-Coriolis equations with spatially almost periodic initial data

We survey solvability results on the Navier-Stokes equations with or without the Coriolis force when initial velocity may not decay at the spatial infinity. A typical such datum is a spatially almost periodic datum. We introduce a suitable space so that the life span can be taken uniformly in the magnitude of rotation. A global existence result for small initial data is given for nondecaying initial data for the Navier-Stokes-Coriolis equations.