Geodesic
Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions
Electronic journal of differential equations, Tome 2003 (2003)
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.
Classification : 76E06, 80A22, 82B26, 76D05
Keywords: phase-field, phase transition, solidification, convection, Navier-Stokes equations 
@article{EJDE_2003__2003__a105,
     author = {Boldrini,  Jos\'e Luiz and Dias Vaz,  Cristina L\'ucia},
     title = {Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1034.76057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a105/}
}
TY  - JOUR
AU  - Boldrini,  José Luiz
AU  - Dias Vaz,  Cristina Lúcia
TI  - Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions
JO  - Electronic journal of differential equations
PY  - 2003
VL  - 2003
UR  - http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a105/
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%A Dias Vaz,  Cristina Lúcia
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%J Electronic journal of differential equations
%D 2003
%V 2003
%U http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a105/
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%F EJDE_2003__2003__a105
Boldrini,  José Luiz; Dias Vaz,  Cristina Lúcia. Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a105/