Dispersive effects of weakly compressible and fast rotating inviscid fluids
Résumé
We consider a system describing the motion of an isentropic, inviscid, weakly com-pressible, 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^∞([0, T ]; H^s(R^3)) , where T is independent of the Rossby and Mach numbers. Moreover, using Strichartz-type estimates, we prove that the solution is almost global, i.e. its lifespan is of the order of ε^(−α) , α > 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.
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