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The ( p - q) Coupled Fluid-Energy Systems

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Advances in Mathematical Fluid Mechanics

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Abstract

We investigate the nonlinear coupled system of elliptic partial differential equations which describes the fluid motion and the energy transfer what we call the ( p - q) coupled fluid-energy system due to p and q coercivity parameters correlated to the motion and heat fluxes, respectively. Due to the simultaneous action of the convective-radiation effects on a part of the boundary, such system leads to a boundary value problem. We present existence results of weak solutions under different constitutive laws for the Cauchy stress tensor with p > 3n/(n + 2), in a n-dimensional space. If the Joule effect is neglected in the energy equation, the existence result is stated for a broader class of fluids such that p > 2n/(n + 1), and related q-coercivity parameter to the heat flux.

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Author information

Authors and Affiliations

  1. Department of Mathematics and CMAF, Sciences Faculty, University of Lisbon, 1749-016, Lisboa, Portugal

    Luisa Consiglieri

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  1. Luisa Consiglieri
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Correspondence to Luisa Consiglieri .

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Editors and Affiliations

  1. Interdisziplinäres Zentrum für, Universität Heidelberg, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Rolf Rannacher

  2. Depto. Mathemática, Istituto Superior Técnico, Av. Rovisco Pais, Lisboa, 1049-001, Portugal

    Adélia Sequeira

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Consiglieri, L. (2010). The ( p - q) Coupled Fluid-Energy Systems. In: Rannacher, R., Sequeira, A. (eds) Advances in Mathematical Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04068-9_11

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