Dispersive effect of the Coriolis force and the local well-posedness for the Navier-Stokes equations in the rotational framework

We consider the initial value problems for the Navier-Stokes equations with the Coriolis force. We prove the local in time existence and uniqueness of the mild solution for every Ω ∈ R \ {0} and u₀ ∈ H^s(R³)³ with s > 1/2. Furthermore, we give a lower bound of the existence time in terms of |Ω|. (formula presented) It follows from our lower bound that the existence time T of the solution can be taken arbitrarily large provided the speed of rotation |Ω| is sufficiently fast.