Yoshiyuki Kagei, Kyushu University, Fukuoka, Japan We consider the compressible Navier-Stokes equation for barotropic flow in an infinite layer whose boundary is periodic in the horizontal variables. For a sufficiently small external force that is periodic in the horizontal variables, there exists a periodic stationary solution to the system. It will be shown that the stationary solution is stable under sufficiently small local perturbtaions and that the perturbation behaves diffusively in large time, like a solution of a heat equation in the horizontal variables.

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