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Existence and Uniqueness of Solution to the Two-Phase Stefan Problem with Convection

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Abstract

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.

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Acknowledgements

We are indebted to anonymous referees for pertinent suggestions which permitted us to improve the presentation. V.B. acknowledges the hospitality of Laboratoire de mathématiques Raphaël Salem where this work was initiated in January 2020.

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Authors and Affiliations

  1. Octav Mayer Institute of Mathematics of the Romanian Academy, Iasi, Romania

    Viorel Barbu

  2. Normandie University, INSA de Rouen Normandie, LMI (EA 3226 - FR CNRS 3335), France 685 Avenue de l’Université, 76801, Saint-Étienne-du-Rouvray, France

    Ioana Ciotir

  3. Laboratoire de Mathématiques Raphaël Salem UMR 6085 CNRS-Université de Rouen Normandie Avenue de l’Université, BP.12, 76801, Saint-Étienne-du-Rouvray, France

    Ionut Danaila

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  1. Viorel Barbu
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  2. Ioana Ciotir
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Correspondence to Ioana Ciotir.

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I.C. and I.D. acknowledge financial support from the French ANR grant ANR-18-CE46-0013 QUTE-HPC and the European Union with the European regional development fund (ERDF, HN0002137 and 18P03390/18E01750/18P02733) and by the Normandie Regional Council (via the M2NUM and M2SiNum projects).

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Barbu, V., Ciotir, I. & Danaila, I. Existence and Uniqueness of Solution to the Two-Phase Stefan Problem with Convection. Appl Math Optim 84 (Suppl 1), 123–157 (2021). https://doi.org/10.1007/s00245-021-09764-w

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