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

2021/06/25 by Gabriele Sbaiz, Sbaiz, Gabriele
Engineering · Mathematics · #35B25 #35B40 #35Q86 #76M45 #76U05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.2106.13699

openalex publication_date 2021/06/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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.

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