Half space problem of the system of compressible adiabatic flow through porous media in multi-D

In this paper, we consider the half space problem for the system of compressible adiabatic flow through porous media in 2-D and 3-D. Combining energy method, Green's function method and bootstrap method, one establishes the decaying energy estimates which lead to global existence and optimal L2 decaying rate of the solution. Finally, for more large time information especially in spatial variables, one applies Green's function, solution representation obtained by Duhamel's principle and a priori estimate from energy method to obtain the space time pointwise structure of the solution.