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In the present paper, we study the fast rotation limit for thedensity-dependent incompressible Euler equations in two space dimensions withthe presence of the Coriolis force. In the case when the initial densities aresmall perturbation of a constant profile, we show the convergence of solutionstowards the solutions of a quasi-homogeneous incompressible Euler system. Theproof relies on a combination of uniform estimates in high regularity normswith a compensated compactness argument for passing to the limit. Thistechnique allows us to treat the case of ill-prepared initial data.

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