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.
DISPERSIVE EFFECTS OF WEAKLY COMPRESSIBLE AND FAST ROTATING INVISCID FLUIDS
Scrobogna S
2018-01-01
Abstract
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.| File | Dimensione | Formato | |
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