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1 LMRS - Laboratoire de Mathématiques Raphaël Salem 2 IMB - Institut de Mathématiques de Bordeaux

Abstract : 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^sR^3 , s > 5-2. We prove that the system admits a unique local strong solution in L^∞0, T ; H^sR^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.





Autor: Van-Sang Ngo - Stefano Scrobogna -

Fuente: https://hal.archives-ouvertes.fr/



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