an:02033629
Zbl 1034.76057
Boldrini, Jos?? Luiz; Dias Vaz, Cristina L??cia
Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions
EN
Electron. J. Differ. Equ. 2003, Paper No. 109, 25 p. (2003).
00094199
2003
j
76T99 80A22 76R10 76D03 35Q30 35R35
weak solutions; phase transition; natural convection; non-stationary solidification; nonlinear heat equation; modified Navier-Stokes equations; buoyancy; Boussinesq approximation; Carman-Koseny term; mushy regions; free boundary problem
Summary: We study existence and regularity of weak solutions of a phase field type model for pure material solidification in the presence of natural convection. We assume that a non-stationary solidification occurs in a two-dimensional bounded domain. The governing equations are the phase field equation coupled with a nonlinear heat equation and modified Navier-Stokes equations. 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 hold only in the non-solid regions, which are not known a priori, we have a free boundary problem.