On time analyticity of the Navier–Stokes equations in a rotating frame with spatially almost periodic data

We consider the Navier–Stokes equations with the Coriolis force when initial data may not decrease at spatial infinity so that almost periodic data is allowed. We prove that the local-in-time solution is analytic in time when initial data are in FM0FM0, the Fourier preimage of the space of all finite Radon measures with no point mass at the origin. When the initial data are almost periodic, this implies that the complex amplitude is analytic in time. In particular, a new mode cannot be created at any positive time.