Global existence and large time behavior for the system of compressible adiabatic flow through porous media in R3R3

The system of compressible adiabatic flow through porous media is considered in R3R3 in the present paper. The global existence and uniqueness of classical solutions are obtained when the initial data is near its equilibrium. We also show that the pressure of the system converges to its equilibrium state at the same L2L2-rate (1+t)−34 as the Navier–Stokes equations without heat conductivity, but the velocity of the system decays at the L2L2-rate (1+t)−54, which is faster than the L2L2-rate (1+t)−34 for the Navier–Stokes equations without heat conductivity (Duan and Ma, 2008 [3]).