Asymptotics for the inviscid rotating stably stratified Boussinesq equations in a 3D layer

Abstract We consider the initial value problem of the inviscid Boussinesq equations for rotating stably stratified flows in a three-dimensional infinite layer. We establish the long-time existence and uniqueness of classical solutions under the condition that both the rotating speed and the buoyancy frequency are sufficiently high. Furthermore, we consider the asymptotic limit of rapid rotation and strong stratification, and prove that the long-time solution strongly converges to that of the quasi-geostrophic equations.