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We consider the double-diffusive convection phenomenon and analyze the governing equations. A system of partial differential equations describing the convective flow arising when a layer of fluid with a dissolved solute is heated from below is considered. The problem is placed in a functional analytic setting in order to prove a theorem on existence, uniqueness and continuous dependence on initial data of weak solutions in the class $([0,\infty );H)\cap L{²}_{loc}({ℝ}^{+};V)$. This theorem enables us to show that the infinite-dimensional...