Global solutions for the system of a viscous two-fluid model

Abstract

In this paper, we consider a viscous compressible two-fluid model with a pressure law that depends on two variables. We establish the existence theory for the global solution of this system within the $H^N\left(R^3\right)$-framework $(N\ge 2)$, assuming that the $H^2\left(R^3\right)$-norm of the initial perturbation is small. The energy method combined with the low-frequency and high-frequency decomposition is used to derive the decay of the solution and hence the global existence. As a byproduct, we obtain the $L^2$-$L^2$ convergence rates for the solution.