Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions
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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.
CitationBoldrini, J. L., & Dias Vaz, C. L. (2003). 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, 2003(109), pp. 1-25.
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