Asymptotic Analysis of Rapidly Rotating 2-D Non-Homogeneous Incompressible Euler Equations in Bounded Domain

Source abstract

In this paper, we investigate the fast rotation limit of the density-dependent incompressible Euler equations in two-dimensional bounded domain. The case considered here is the so-called quasi-homogeneous regime in which the initial density is a small perturbation of a constant state. We show that solution of the original system will convergence to the solution of the quasi-homogeneous incompressible Euler system. The proof is based on a combination of uniform estimates in $H^s$ norms with a compensated compactness argument. No well-prepared restrictions are imposed on the initial data.