# American Institute of Mathematical Sciences

doi: 10.3934/cpaa.2021084

## On the invariant region for compressible Euler equations with a general equation of state

 1 Iowa State University, Mathematics Department, Ames, IA 50011, USA 2 Otto-von-Guericke-Universität, Universitätsplatz 2, Magdeburg, 39106, Germany

* Corresponding author

Dedicated to Professor Shuxing Chen on the occasion of his 80th birthday

Received  February 2021 Revised  April 2021 Published  May 2021

Fund Project: Hailiang Liu was partially supported by the National Science Foundation under Grant DMS1812666

The state space for solutions of the compressible Euler equations with a general equation of state is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. An invariant region of the resulting Euler system is identified and the convexity property of this region is justified by using only very minimal thermodynamical assumptions. Finally, we show how an invariant-region-preserving (IRP) limiter can be constructed for use in high order finite-volume type schemes to solve the compressible Euler equations with a general constitutive relation.

Citation: Hailiang Liu, Ferdinand Thein. On the invariant region for compressible Euler equations with a general equation of state. Communications on Pure & Applied Analysis, doi: 10.3934/cpaa.2021084
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