We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space R-3, with initial data belonging to H-s (R-3), s > 5/2. We prove that the system admits a unique local strong solution in L-infinity ([0, T]; H-s (R-3)), where T is independent of the Rossby and Mach numbers. Moreover, using Strichartz-type estimates, we prove the longtime existence of the solution, i.e. its lifespan is of the order of epsilon(-alpha), alpha > 0, without any smallness assumption on the initial data (the initial data can even go to infinity in some sense), provided that the rotation is fast enough.
