| Abstract: |
| In this talk, we are concerned with a class of singular perturbation problems for viscous weakly compressible flows, which undergo the action of a strong Coriolis force.
We want to perform the incompressible and fast rotation limits simultaneously, when the Mach and Rossby numbers may have different orders of magnitude.
We will show how weak compactness methods allow to handle the multiple scales appearing in the system, and to prove convergence for a wide range of parameters.
The key point is to exploit the algebraic structure of the system, and especially a compactness property hidden in the system of acoustic-Poincar\`e waves.
The drawback of this technique is that it does not yield any rate of convergence of the solutions to the primitive system towards the solutions of the target problem, which in fact is
(in some cases) underdetermined. |
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