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

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.