Electron. J. Diff. Eqns., Vol. 2003(2003), No. 109, pp. 1-25.

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

Jose Luiz Boldrini & Cristina Lucia Dias Vaz

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.

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Jose Luiz Boldrini
Department of Mathematics
UNICAMP-IMECC, Brazil
email: boldrini@ime.unicamp.br
Cristina Lucia Dias Vaz
Department of Mathematics
Universidade Federal do Para, Brazil
email: cvaz@ufpa.br

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