Attractors for autonomous double-diffusive convection systems based on Brinkman–Forchheimer equations

In this paper, we consider the existence of global attractor and exponential attractor for some dynamical system generated by nonlinear parabolic equations in bounded domains with the dimension N≤4 which describe double-diffusive convection phenomena in a porous medium. We deal with both of homogeneous Dirichlet and Neumann boundary condition cases. Especially, when Neumann condition is imposed, we need some assumptions and restrictions for the external forces and the average of initial data, since the mass conservation law holds.