Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/102343
Type: Artigo
Title: Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions
Author: José Luiz Boldrini
Cristina Lúcia 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.
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
Subject: Soluções fracas (Matemática)
Solidificação
Navier-Stokes, Equações de
Problemas de valores de contorno
Country: Estados Unidos
Editor: Texas State University/Department of Mathematics
Citation: Electronic Journal Of Differential Equations. , v. 2003, n. , p. 1 - 25, 2003.
Rights: aberto
Identifier DOI: 0
Address: https://ejde.math.txstate.edu/Volumes/2003/109/abstr.html
Date Issue: 2003
Appears in Collections:IMECC - Artigos e Outros Documentos

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