Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data

Abstract: In this paper, we consider a compressible two-fluid system with a common velocity field and algebraic pressure closure in dimension one. Existence, uniqueness and stability of global weak solutions to this system are obtained with arbitrarily large initial data. Making use of the uniform-in-time bounds for the densities from above and below, exponential decay of weak solution to the unique steady state is obtained without any smallness restriction to the size of the initial data. In particular, our results show that degeneration to single-fluid motion will not occur as long as in the initial distribution both components are present at every point.