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Decay estimates for the Brinkman‐Forchheimer equations in a semi‐infinite pipe

In this paper, we consider the Brinkman‐Forchheimer equations in a semi‐infinite pipe. A second order differential inequality is derived which leads to an exponential decay estimate for the energy E (z,t) defined in (3.1) under appropriate initial and boundary conditions. We also indicate how to establish the explicit bound for the total energy.