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Continuous dependence and uniqueness for heat-conducting viscous fluids in bounded domains

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Abstract

Continuous dependence upon the initial data for solutions to initial-boundary value problems in bounded domains is investigated in connection with heat-conducting viscous fluids with hidden variables. It turns out that, in the case of incompressible fluids, the initial-boundary conditions guaranteeing the continuous dependence of classical solutions on the initial data, the body force, and the heat supply are the most natural generalization of the usual ones. Indeed, the boundary data for the hidden variables are the strict counterpart of those for the stress tensor and the heat supply in the standard theory.

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Authors and Affiliations

  1. Istituto di Matematica «S. Pincherle», Piazza di Porta S. Donato, 5, 40127, Bologna

    F. Franchi & A. Morro

  2. Facoltà di Ingegneria, Istituto di Matematica, 16129, Genova

    F. Franchi & A. Morro

Authors
  1. F. Franchi
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  2. A. Morro
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Franchi, F., Morro, A. Continuous dependence and uniqueness for heat-conducting viscous fluids in bounded domains. Rend. Circ. Mat. Palermo 33, 145–158 (1984). https://doi.org/10.1007/BF02844610

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  • DOI: https://doi.org/10.1007/BF02844610

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