Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid

We consider a compressible viscous fluid affected by external forces of general form which are small and smooth enough in suitable norms in R³. In Shibata and Tanaka [Y. Shibata, K. Tanaka, On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance, J. Math. Soc. Japan 55 (2003) 797-826], we proved the unique existence and some regularity of the steady flow and its globally in-time stability with respect to a small initial disturbance in the H³-framework. In this paper, we investigate the rate of the convergence of the non-stationary flow to the corresponding steady flow when the initial data are small enough in the H³ and also belong to L_{6 / 5}.