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

Gabriele Sbaiz (1, 2)

1 Dipartimento di Matematica e Geoscienze [Trieste]
2 EDPA - Équations aux dérivées partielles, analyse

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.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Gabriele Sbaiz. Fast rotation limit for the 2-D non-homogeneous incompressible Euler equations. Journal of Mathematical Analysis and Applications, 2021, 512 (1), pp.126140. ⟨10.1016/j.jmaa.2022.126140⟩. ⟨hal-03272157⟩