# American Institute of Mathematical Sciences

March  2012, 5(1): 185-201. doi: 10.3934/krm.2012.5.185

## H-Theorem for nonlinear regularized 13-moment equations in kinetic gas theory

 1 Center for Computational Engineering Science, RWTH Aachen University, Schinkelstr.2, 52062 Aachen, Germany

Received  May 2011 Revised  July 2011 Published  January 2012

The regularized 13-moment equations (R13) are a successful macroscopic model to describe non-equilibrium gas flows in rarefied or micro situations. Even though the equations have been derived for the nonlinear case and many examples demonstrate the usefulness of the equations, sofar, the important property of an accompanying entropy law could only be shown for the linearized equations [Struchtrup&Torrilhon, Phys. Rev. Lett. 99, (2007), 014502]. Based on an approach suggested by Öttinger [Phys. Rev. Lett. 104, (2010), 120601], this paper presents a nonlinear entropy law for the R13 system. In the derivation the variables and equations of the R13 system are nonlinearily extended such that an entropy law with non-negative production can be formulated. It is then demonstrated that the original R13 system is included in the new equations.
Citation: Manuel Torrilhon. H-Theorem for nonlinear regularized 13-moment equations in kinetic gas theory. Kinetic & Related Models, 2012, 5 (1) : 185-201. doi: 10.3934/krm.2012.5.185
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