Boldrini, Jose LuizDias Vaz, Cristina Lucia2021-01-272021-01-272003-11-03Boldrini, 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. <i>Electronic Journal of Differential Equations, 2003</i>(109), pp. 1-25.1072-6691https://hdl.handle.net/10877/13160We 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.Text25 pages1 file (.pdf)enAttribution 4.0 InternationalPhase-fieldPhase transitionsSolidificationConvectionNavier-Stokes equationsArticle