Type of Publication:  Journal article 
Publication status:  Published 
Author:  Freistühler, Heinrich 
Year of publication:  2019 
Published in:  Archive for Rational Mechanics and Analysis ; 232 (2019), 1.  pp. 473488.  ISSN 00039527.  eISSN 14320673 
DOI (citable link):  https://dx.doi.org/10.1007/s0020501813252 
Summary: 
A relativistic fluid is called barotropic if its internal energy ρ and its pressure p are onetoone related; it is called isentropic if ρ and p are both onetoone related to the fluid’s particle number density n. Deriving Godunov variables and 4potentials for the relativistic Euler equations of perfect barotropic fluids, this paper first pursues ideas on symmetric hyperbolicity going back to Godunov and Boillat that Ruggeri and Strumia have elaborated as their theory of convex covariant density systems. The associated additional balance law (not a conservation law in the presence of shock waves) has different interpretations for different fluids. Among all barotropic fluids, we notably distinguish those for which this extra equation coincides with the second law of thermodynamics. We characterize these ‘thermobarotropic’ fluids, a class which comprises in particular the socalled pure radiation gas used in cosmology. The paper also shows that isentropic fluids are not thermobarotropic and that, like in the nonrelativistic case, they cannot simultaneously satisfy the conservation laws of mass, momentum, and energy, as soon as shock waves occur. Curiously, relativistic isentropic flows which conserve energy and momentum generate mass across shock waves; this is a counterpart of the wellknown fact that across shock waves, nonrelativistic isentropic flows which conserve mass and momentum dissipate energy.

Subject (DDC):  510 Mathematics 
Bibliography of Konstanz:  Yes 
Refereed:  Unknown 
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FREISTÜHLER, Heinrich, 2019. Relativistic Barotropic Fluids : A Godunov–Boillat Formulation for their Dynamics and a Discussion of Two Special Classes. In: Archive for Rational Mechanics and Analysis. 232(1), pp. 473488. ISSN 00039527. eISSN 14320673. Available under: doi: 10.1007/s0020501813252
@article{Freistuhler201904Relat44862, title={Relativistic Barotropic Fluids : A Godunov–Boillat Formulation for their Dynamics and a Discussion of Two Special Classes}, year={2019}, doi={10.1007/s0020501813252}, number={1}, volume={232}, issn={00039527}, journal={Archive for Rational Mechanics and Analysis}, pages={473488}, author={Freistühler, Heinrich} }
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