In this paper, the global solvability of the initial boundary value problem and the periodic problem are discussed for a doublediffusive convection system under the homogeneous Neumann boundary condition in a bounded domain. This system is coupled with the so-called Brinkman-Forchheimer equations, which is similar to the Stokes equations and contains some convection terms similar to that in the Navier-Stokes equations. However, in contrast to the Navier-Stokes equations, it is shown that the

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... bal solvability in L 2 -spaces holds true for the 3-dimensional problems.