%0 Journal Article
%T Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions
%A Jose Luiz Boldrini
%A Cristina Lucia Dias Vaz
%J Electronic Journal of Differential Equations
%D 2003
%I Texas State University
%X We study the existence and regularity of weak solutions of a phase field type model for pure material solidification in presence of natural convection. We assume that the non-stationary solidification process occurs in a two dimensional bounded domain. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and a modified Navier-Stokes equation. These equations include buoyancy forces modelled by Boussinesq approximation and a Carman-Koseny term to model the flow in mushy regions. Since these modified Navier-Stokes equations only hold in the non-solid regions, which are not known a priori, we have a free boundary-value problem.
%K Phase-field
%K phase transition
%K solidification
%K convection
%K Navier-Stokes equations.
%U http://ejde.math.txstate.edu/Volumes/2003/109/abstr.html