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Well-Posedness of a Gas—Solid Phase Transition Problem

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Abstract.

A new model for liquid—solid phase transitions within the frame of complete Navier—Stokes equations in a liquid phase is proposed. It takes into account such properties of liquid as compressibility, viscosity, and heat conductivity. The local existence and uniqueness of a smooth solution to the related initial-boundary value problem is proved.

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences, Lavrentyev pr. 15, Novosibirsk 630090, Russia, e-mail: kaliev@hydro.nsc.ru, , , , , , RU

    I. A. Kaliev

  2. Lavrentyev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences, Lavrentyev pr. 15, Novosibirsk 630090, Russia, e-mail: kazhikhov@hydro.nsc.ru, , , , , , RU

    A. V. Kazhikhov

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  1. I. A. Kaliev
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  2. A. V. Kazhikhov
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Accepted: August 11, 1999.

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Kaliev, I., Kazhikhov, A. Well-Posedness of a Gas—Solid Phase Transition Problem. J. math. fluid mech. 1, 282–308 (1999). https://doi.org/10.1007/s000210050012

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  • DOI: https://doi.org/10.1007/s000210050012

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