Asymptotic dynamics in double-diffusive convection

Miko/laj Piniewski¹

¹ Institute of Applied Mathematics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland and Department of Hydraulic Engineering and Environmental Restoration Warsaw University of Life Sciences Nowoursynowska 159 02-787 Warszawa, Poland

Applicationes Mathematicae, Tome 35 (2008) no. 2, pp. 223-245.

Résumé

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.

Détail

DOI : 10.4064/am35-2-7

Keywords: consider double diffusive convection phenomenon analyze governing equations system partial differential equations describing convective flow arising layer fluid dissolved solute heated below considered problem placed functional analytic setting order prove theorem existence uniqueness continuous dependence initial weak solutions class mathcal infty cap loc mathbb theorem enables infinite dimensional dynamical system generated double diffusive convection equations has global attractor which long term dynamics solutions focused