# American Institute of Mathematical Sciences

May  2013, 12(3): 1341-1347. doi: 10.3934/cpaa.2013.12.1341

## On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state

 1 Universitat Pompeu Fabra, Dept. de Tecnologies de la Informació i les Comunicacions, C/Tànger 122-140, 08018 Barcelona, Spain

Received  April 2012 Revised  May 2012 Published  September 2012

We show that a pair of conjectures raised in [11] concerning the construction of normal solutions to the relativistic Boltzmann equation are valid. This ensures that the results in [11] hold for any range of positive temperatures and that the relativistic Euler system under the kinetic equation of state is hyperbolic and the speed of sound cannot overcome $c/\sqrt{3}$.
Citation: Juan Calvo. On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1341-1347. doi: 10.3934/cpaa.2013.12.1341
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