An Existence Result for a Stochastic Stefan Problem With Mushy Region and Turbulent Transport Noise

TL;DR

This paper proves the existence of a martingale solution for a stochastic Stefan problem that includes a mushy region and turbulent transport noise, using an L2 space framework tailored to the turbulent operator.

Contribution

It introduces a novel existence proof for a complex stochastic Stefan problem with turbulence and mushy regions, utilizing an L2 space approach for the first time.

Findings

Existence of a martingale solution established.

L2 space is effective for turbulent noise analysis.

Model captures complex phase change with turbulence effects.

Abstract

This work is devoted to the proof of the existence of a martingale solution for a complex version of the stochastic Stefan problem. This particular formulation incorporates two important features: a mushy region and turbulent transport within the liquid phase. While our approach bears similarities to porous media equations, it differs in a crucial aspect. Instead of using the typical framework for such equations, we have chosen to work within an L2 space. This choice is motivated by the nature of the operator that characterizes the turbulent noise in our model. The L2 space provides a more natural and appropriate setting for handling this specific operator, allowing us to better capture and analyze the turbulent transport phenomena in the liquid phase of the Stefan problem.