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The damped Navier-Stokes equations (DNS) describe the flow with the resistance to the motion of flow in a porous media. This monograph is concerned with the 3D inhomogeneous Navier-Stokes equations with damping which are more practical and useful in the real world.We prove the existence and uniqueness of weak solutions to the 3D damped Navier-Stokes equations with variable exponent and inhomogeneous boundary condition. And we show the existence and uniqueness of the strong solutions to the inhomogeneous damped Navier-Stokes equations in the whole space.