Seminar on partial differential equations

On a singular limit for the stratified compressible Euler system

We consider a singular limit for the compressible Euler system in the low Mach number regime driven by a large external force. We show that any dissipative measure-valued solution approaches a solution of the lake equation in the asymptotic regime of low Mach and Froude numbers. The result holds for the ill-prepared initial data creating rapidly oscillating acoustic waves. We use dispersive estimates of Strichartz type to eliminate the effect of the acoustic waves in the asymptotic limit.