Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 109, pp. 1-25.

Title: Existence and regularity of solutions of a phase field model
       for solidification with convection of pure materials in  
       two dimensions

Authors: Jose Luiz Boldrini      (UNICAMP-IMECC, Brazil)
         Cristina Lucia Dias Vaz (Univ. Federal do Para, Brazil)

Abstract: 
  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.
 
Submitted September 14, 2001. Published November 3, 2003.
Math Subject Classifications: 76E06, 80A22, 82B26, 76D05.
Key Words: Phase-field; phase transition; solidification; convection;
           Navier-Stokes equations.