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In this paper, spatial decay estimates for the time dependent compressible viscous isentropic flow in a semi-infinite three dimensional pipe are derived. An upper bound for the total energy in terms of the initial boundary data is obtained as well. The results established in this paper may be viewed as a version of Saint-Venant's principle in transient compressible Navier-Stokes flow. © 2011 The Korean Mathematical Society.

SPATIAL DECAY BOUNDS OF SOLUTIONS TO THE NAVIER-STOKES EQUATIONS FOR TRANSIENT COMPRESSIBLE VISCOUS FLOW