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<p>This paper is devoted to the study of a non-isothermal phase-field model to describe the microstructure evolution for sea-ice growth. The model consists of a system of non-linear parabolic equations. The existence of global weak solutions to an initial-boundary value problem of this model is established by means of the Galerkin method and the energy method. The uniqueness and regularity are also studied under certain conditions on the nonlinearities. Moreover, we show that the model has a bounded absorbing set. Finally, a numerical calculation is performed, which reveals dendritic growth morphology in the solid-liquid interface during solidification of seawater.</p>

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Weak Solutions and Simulations to a Phase-field Model for Sea-ice Growth

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Md Akram Hossain,
  • Peicheng Zhu

摘要

This paper is devoted to the study of a non-isothermal phase-field model to describe the microstructure evolution for sea-ice growth. The model consists of a system of non-linear parabolic equations. The existence of global weak solutions to an initial-boundary value problem of this model is established by means of the Galerkin method and the energy method. The uniqueness and regularity are also studied under certain conditions on the nonlinearities. Moreover, we show that the model has a bounded absorbing set. Finally, a numerical calculation is performed, which reveals dendritic growth morphology in the solid-liquid interface during solidification of seawater.