Analysis of weak solutions of a phase-field model for sea ice evolution

Abstract

This paper is devoted to the study of the well-posedness of an initial-boundary value problem (IVBP) for a three-dimensional two-phase system, which is a phase-field model consisting of two coupled parabolic equations and is used to describe the solid–liquid phase transition of sea ice growth. First, we give the derivation of this model. Then, we prove the global-in-time existence and uniqueness of the weak solutions to the IBVP by means of the Galerkin approximation argument and the energy method. In addition, we establish a maximum principle that guarantees the model is physically consistent. Finally, the regularity of weak solutions is also established.