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On the Navier-Stokes Equations with Energy-Dependent Nonlocal Viscosities

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Abstract

We discuss the mathematical modeling of incompressible viscous flows for which the viscosity depends on the total dissipation energy. In the two-dimensional periodic case, we begin with the case of temperature-dependent viscosities with very large thermal conductivity in the heat convective equation, in which we obtain the Navier-Stokes system coupled with an ordinary differential equation involving the dissipation energy as the asymptotic limit. Letting further the latent heat to vanish, we derive the Navier-Stokes equations with a nonlocal viscosity depending on the total dissipation of energy. Bibliography: 7 titles.

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REFERENCES

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Authors and Affiliations

  1. Department of Mathematics and CMAF, University of Lisboa, Portugal

    L. Consiglieri & J. F. Rodrigues

  2. St. Petersburg Department, Steklov Mathematical Institute, St. Petersburg, Russia

    T. Shilkin

Authors
  1. L. Consiglieri
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  2. J. F. Rodrigues
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  3. T. Shilkin
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Dedicated to V. A. Solonnikov on the occasion of his 70th birthday

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 71–91.

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Consiglieri, L., Rodrigues, J.F. & Shilkin, T. On the Navier-Stokes Equations with Energy-Dependent Nonlocal Viscosities. J Math Sci 130, 4814–4826 (2005). https://doi.org/10.1007/s10958-005-0378-6

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  • DOI: https://doi.org/10.1007/s10958-005-0378-6

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