Weak Solutions to an Initial-Boundary Value Problem of a Consistent Three-phase-field Model

Abstract

Global warming has caused the melting of glaciers, especially the Greenland sea ice which is a great threat to human beings. The phase-field method is used to describe the evolution of multi-phase microstructure of Greenland sea ice. This paper shall investigate the global existence, uniqueness and regularity of weak solutions to an initial-boundary value problem for a three-phase-field model based on criteria that lead to both physical and mathematical consistency. For global solutions, it is calculated by applying the method of continuation of local solutions. This model allows for the formulation of spurious phases, which is completely consistent with physical reality.