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On a singular limit for the compressible rotating Euler system. (English) Zbl 1448.35368

Summary: The work addresses a singular limit for a rotating compressible Euler system in the low Mach number and low Rossby number regime. Based on the concept of dissipative measure-valued solution, the quasi-geostrophic system is identified as the limit problem in the case of ill-prepared initial data. The ill-prepared initial data will cause rapidly oscillating acoustic waves. Using dispersive estimates of Strichartz type, the effect of the acoustic waves in the asymptotic limit is eliminated.

MSC:

35Q30 Navier-Stokes equations
35Q86 PDEs in connection with geophysics
76N06 Compressible Navier-Stokes equations
76U60 Geophysical flows
76U65 Rossby waves
76Q05 Hydro- and aero-acoustics
86A05 Hydrology, hydrography, oceanography
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