Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 109, pp. 1-25.
Title: Existence and regularity of solutions of a phase field model
for solidification with convection of pure materials in
two dimensions
Authors: Jose Luiz Boldrini (UNICAMP-IMECC, Brazil)
Cristina Lucia Dias Vaz (Univ. Federal do Para, Brazil)
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.