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We consider a system describing the motion of an isentropic, inviscid, weaklycom-pressible, fast rotating fluid in the whole space R^3 , with initial databelonging to H^s(R^3) , s \textgreater{} 5/2. We prove that the system admits aunique local strong solution in L^$\infty$([0, T ]; H^s(R^3)) , where T isindependent of the Rossby and Mach numbers. Moreover, using Strichartz-typeestimates, we prove that the solution is almost global, i.e. its lifespan is ofthe order of $\epsilon$^(--$\alpha$) , $\alpha$ \textgreater{} 0, without anysmallness assumption on the initial data (the initial data can even go toinfinity in some sense), provided that the rotation is fast enough.

Dispersive effects of weakly compressible and fast rotating inviscid fluids