Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions

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dc.contributor.authorBoldrini, Jose Luiz
dc.contributor.authorDias Vaz, Cristina Lucia
dc.date.accessioned2021-01-27T21:43:26Z
dc.date.available2021-01-27T21:43:26Z
dc.date.issued2003-11-03
dc.description.abstractWe 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.identifier.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. <i>Electronic Journal of Differential Equations, 2003</i>(109), pp. 1-25.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13160
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectPhase-field
dc.subjectPhase transitions
dc.subjectSolidification
dc.subjectConvection
dc.subjectNavier-Stokes equations
dc.titleExistence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensionsen_US
dc.typeArticle

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