Weak-renormalized solutions for a system that models non-isothermal solidification

Abstract

The aim of this paper is to prove the existence of weak-renormalized solutions to a system of the Navier-Stokes-Boussinesq kind. This system may be regarded as a modified version of the non-isothermal solidification problem with melt convection. This task will be accomplished satisfactorily in the two-dimensional case. Some nontrivial and deep difficulties will be found, however, in three dimensions in space.