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The Brinkman-Fourier system with ideal gas equilibrium

  • * Corresponding author: Jan-Eric Sulzbach

    * Corresponding author: Jan-Eric Sulzbach
The authors are supported by NSF grant DMS-1714401 and by United States-Israel Binational Science Foundation grant BSF 2024246
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  • In this work, we will introduce a general framework to derive the thermodynamics of a fluid mechanical system, which guarantees the consistence between the energetic variational approaches with the laws of thermodynamics. In particular, we will focus on the coupling between the thermal and mechanical forces. We follow the framework for a classical gas with ideal gas equilibrium and present the existences of weak solutions to this thermodynamic system coupled with the Brinkman-type equation to govern the velocity field.

    Mathematics Subject Classification: Primary: 35D30, 35Q79; Secondary: 76N10.


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