Global solvability of some double-diffusive convection system coupled with Brinkman-Forchheimer equations

Abstract

In this paper, the global solvability of the initial boundary value problem and the periodic problem are discussed for double-diffusive convection systems under the homogeneous Neumann boundary condition in a bounded domain. This system is coupled with the so-called Brinkman-Forchheimer equation, which is similar to the Stokes equation and contains some convection terms similar to that in Navier-Stokes equations. However, in contrast to Navier-Stokes equations, it is shown that the global solvability in L^2 -spaces holds true for the 3-dimensional problems.