Electron. J. Diff. Eqns., Vol. 2003(2003), No. 109, pp. 125.
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 nonstationary
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 NavierStokes
equation. These equations include buoyancy forces modelled by
Boussinesq approximation and a CarmanKoseny term to model the
flow in mushy regions. Since these modified NavierStokes equations
only hold in the nonsolid regions, which are not known a priori,
we have a free boundaryvalue problem.
Submitted September 14, 2001. Published November 3, 2003.
Math Subject Classifications: 76E06, 80A22, 82B26, 76D05.
Key Words: Phasefield, phase transition, solidification, convection,
NavierStokes equations.
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Jose Luiz Boldrini
Department of Mathematics
UNICAMPIMECC, 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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