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).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a5/}
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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__a5/