Structural stability for a thermal convection model with temperature-dependent solubility

TL;DR

This paper investigates the stability of a thermal convection model with temperature-dependent solubility, establishing continuous dependence of solutions on reaction rates in a bounded 2D domain.

Contribution

It provides the first rigorous analysis of how chemical reactions affecting solubility influence thermosolutal convection stability.

Findings

Solution depends continuously on reaction rate

Established a priori bounds for solutions

Applicable to arbitrary temperature-dependent solubility functions

Abstract

We study a problem involving thermosolutal convection in a fluid when the solute concentration is subject to a chemical reaction in which the solubility of the dissolved component is a function of temperature. When the spatial domain is a bounded one in $\mathbb{R}^{2}$ we show that the solution depends continuously on the reaction rate using true \emph{a priori} bounds for the solution when the chemical equilibrium function is an arbitrary function of temperature.