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Convection under low gravity: Correctness of mathematical models

  • Physics Of Contact Line And Wetting/Thermocapillary Flows
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Abstract

The alternative mathematical models of convective fluids flows (the microconvection model of isothermally incompressible fluid, the model of convection of weakly compressible fluid) and the classical Oberbeck-Boussinesq model with temperature dependent viscosity are applicable to investigation of many applied problems of convection: convection under low gravity, in small scales and at fast changes of the boundary thermal regimes. A characteristic property of the alternative mathematical models is the nonsolenoidality of the velocity fields.

Principal issues relating to well/ill posed initial boundary value problems for the mathematical models of convection are considered. For the convection equations of weakly compressible fluid the initial boundary value problem with general temperature condition on the boundary is studied. The analytical result concerning the correctness of this problem is presented: the local theorem of existence of a smooth solution in the classes of the Hoelder functions is proved.

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References

  1. Goncharova, O.N., 2002, “About uniqueness of solution of two-dimensional nonstationary problem for convection equations with temperature dependent viscosity” (in Russian). Differential Equations, 38, 3, 1–9

    MathSciNet  Google Scholar 

  2. V.K. Andreev, O.V. Kaptsov, V.V. Pukhnachov, A.A. Rodionov, Applications of group-theoretical methods in hydrodynamics, 1998, Kluwer Academic Publ. Dordrecht/Boston/London

    MATH  Google Scholar 

  3. Perera, P.S., Sekerka R.F., 1997, “Nonsolenoidal flow in a liquid diffusion couple”. Phys. Fluids, 9, 2, 376–391

    Article  Google Scholar 

  4. Pukhnachov, V.V., 2003, “Hierarchy of the models in the convection theory” (in Russian). Notices of Petersburg Division of Steklov Mathematical Institute, 288, 152–177

    Google Scholar 

  5. Goncharova, O.N., 2005, “Exact solutions of linearized equations of convection of a weakly compressible fluid”. Journal of Applied Mechanics and Technical Physics, 46, 2, 191–201

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Altai State University and Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, Russian

    Olga Goncharova

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  1. Olga Goncharova
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Additional information

Paper was presented on the Second International Topical Team Workshop on TWO-PHASE SYSTEMS FOR GROUND AND SPACE APPLICATIONS October 26–28, 2007, Kyoto, Japan.

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Goncharova, O. Convection under low gravity: Correctness of mathematical models. Microgravity Sci. Technol 19, 113–115 (2007). https://doi.org/10.1007/BF02915769

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  • DOI: https://doi.org/10.1007/BF02915769

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