Optimal decay rates on the solution to the compressible gas–liquid drift-flux model with slip

In this paper, the large time behavior of the solution to the initial-boundary problems for the one-dimensional compressible gas–liquid drift-flux model with slip is studied. Under some suitable smallness conditions upon the initial data, the optimal pointwise upper and lower decay estimates on masses as well as the sharpest decay rates for the norms in terms of the velocity function are obtained. This result generalizes the one in [On the large time behavior of the compressible gas–liquid drift-flux model with slip, Math. Models Methods Appl. Sci. 25 (2015) 2175–2215] by Evje and Wen. The key of the proof is to derive some new global-in-time weighted estimates. Our method can also be easily adopted to the study on the large time behavior of the solution to the one-dimensional compressible Naiver–Stokes equations.