The well posedness of the two-phase Stefan problem with convection is established in \(L^{1}\). First we consider the case with a singular enthalpy and we fix the convection velocity. In the second part of the paper we study the case of a smoothed enthalpy, but the convection velocity is the solution to a Navier-Stokes equation. In the last section we give some numerical illustrations of a physical case simulated using the models studied in the paper.

中文翻译：

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对流两阶段Stefan问题解的存在唯一性

对流的两阶段Stefan问题的适定性在\（L ^ {1} \）中建立。首先，我们考虑具有奇异焓的情况，并确定对流速度。在本文的第二部分中，我们研究了光滑焓的情况，但是对流速度是Navier-Stokes方程的解。在最后一节中，我们使用本文研究的模型对物理情况进行了一些数值说明。