In the present paper, we study the fast rotation limit for the density-dependent incompressible Euler equations in two space dimensions with the presence of the Coriolis force. In the case when the initial densities are small perturbation of a constant profile, we show the convergence of solutions towards the solutions of a quasi-homogeneous incompressible Euler system. The proof relies on a combination of uniform estimates in high regularity norms with a compensated compactness argument for passing to the limit. This technique allows us to treat the case of ill-prepared initial data.

Fast rotation limit for the 2-D non-homogeneous incompressible Euler equations

Gabriele Sbaiz
2022-01-01

Abstract

In the present paper, we study the fast rotation limit for the density-dependent incompressible Euler equations in two space dimensions with the presence of the Coriolis force. In the case when the initial densities are small perturbation of a constant profile, we show the convergence of solutions towards the solutions of a quasi-homogeneous incompressible Euler system. The proof relies on a combination of uniform estimates in high regularity norms with a compensated compactness argument for passing to the limit. This technique allows us to treat the case of ill-prepared initial data.
2022
4-mar-2022
Pubblicato
https://doi.org/10.1016/j.jmaa.2022.126140
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2991819
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