We consider the initial value problem of the 3D inviscid Boussinesq equations for stably stratified fluids. We prove the long-time existence of classical solutions for large initial data when the buoyancy frequency is sufficiently high.
Furthermore, we consider the asymptotic limit of the strong stratification, and show that the long-time classical solution converges to that of 2D incompressible Euler equations in some space-time norms.