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Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid. (English) Zbl 1122.76077
Summary: We consider a compressible viscous fluid affected by external forces of general form which are small and smooth enough in suitable norms in \(\mathbb R^{3}\). In [Y. Shibata and K. Tanaka, J. Math. Soc. Japan 55, No. 3, 797–826 (2003; Zbl 1051.76058)], we proved the unique existence and some regularity of the steady flow and its global in-time stability with respect to a small initial disturbance in the \(H^{3}\)-framework. In this paper, we investigate the rate of convergence of the non-stationary flow to the corresponding steady flow when the initial data are small enough in \(H^{3}\) and also belong to \(L_{6/5}\).

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30 Navier-Stokes equations
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