Dispersive estimates for the Navier-Stokes equations in the rotational framework

Abstract

We consider the Navier-Stokes equations with the Coriolis force (NSC). We establish an improved dispersive estimate for the linear group associated with (NSC), and derive the two-dimensional dispersion effect of the Coriolis forces. As applications, we prove the unique existence of global in time mild solutions for the initial value problem, and the unique existence of time periodic solutions to (NSC).