Large time behavior of solutions to a two phase fluid model in [formula omitted

Abstract

We establish the global existence and large time behavior of a unique classical solution for a two phase fluid model consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations via a drag force, provided the initial data is sufficiently small in H4(R3)∩L1(R3). The main tools employed in the analysis are the spectrum analysis and energy method. Our results show that the classical solution converges to a given equilibrium state at algebra decay rate.