Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

Streszczenie

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 $\mathcal{C}([0,\infty); H) \cap L^2_{\rm loc}(\mathbb{R}^+;V)$. This theorem enables us to show that the infinite-dimensional dynamical system generated by the double-diffusive convection equations has a global attractor on which the long-term dynamics of solutions is focused.