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<p>This work establishes a scaling limit theorem for the Stefan problem incorporating a mushy region, demonstrating that solutions to stochastic variants with turbulent transport terms converge to the solution to a deterministic partial differential equation. The analysis builds upon recent advances in stochastic phase-change modeling and turbulent flow mathematics in [<CitationRef CitationID="CR8">8</CitationRef>]. In the physical interpretation of an ice melting process, our result shows that turbulence accelerates ice melting.</p>

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The Stefan Problem with Mushy Region as a Scaling Limit of Stochastic PDE with Turbulent Transport

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月3日

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  • Ioana Ciotir,
  • Franco Flandoli,
  • Dan Goreac

摘要

This work establishes a scaling limit theorem for the Stefan problem incorporating a mushy region, demonstrating that solutions to stochastic variants with turbulent transport terms converge to the solution to a deterministic partial differential equation. The analysis builds upon recent advances in stochastic phase-change modeling and turbulent flow mathematics in [8]. In the physical interpretation of an ice melting process, our result shows that turbulence accelerates ice melting.