Asymptotic limits of dissipative turbulent solutions to a compressible two-fluid model

Abstract

In this paper we study the asymptotic limits of a compressible two-fluid model in an unbounded domain Ω with general initial data. By applying refined related entropy method and carrying out detailed analysis on the oscillations of velocity, we derive rigorously that the dissipative turbulent solutions (velocity) of the compressible two-fluid model converge to the strong solution of the quasi-geostropic equation when there is a Coriolis force and Ω=R2×T1, and while the two-fluid model has no Coriolis force term and Ω=R3, its solutions converge to the strong solution of incompressible Euler equations.