THE EXISTENCE OF A BOUNDED INVARIANT REGION FOR COMPRESSIBLE EULER EQUATIONS IN DIFFERENT GAS STATES

doi:10.1007/s10473-020-0505-y

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (5): 1229-1239.doi: 10.1007/s10473-020-0505-y

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THE EXISTENCE OF A BOUNDED INVARIANT REGION FOR COMPRESSIBLE EULER EQUATIONS IN DIFFERENT GAS STATES

Weifeng JIANG¹, Zhen WANG²

1. College of Science, China Jiliang University, Hangzhou 310018, China;
2. College of Science, Wuhan University of Technology, Wuhan 430071, China

Received:2019-08-24 Revised:2020-05-13 Online:2020-10-25 Published:2020-11-04
Contact: Zhen WANG E-mail:zwang@whut.edu.cn
Supported by:
The first author was supported by the Natural Science Foundation of Zhejiang (LQ18A010004), the second author was supported by the Fundamental Research Funds for the Central Universities (WUT: 2020IB011).

Abstract

Abstract: In this article, by the mean-integral of the conserved quantity, we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region. Moreover, we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process. Finally, we provide a mathematical example showing that with a special state equation, a bounded invariant region for the non-isentropic process may exist.

Key words: Euler equations, gas dynamic, non-isentropic, existence of invariant region

CLC Number:

35L65

Weifeng JIANG, Zhen WANG. THE EXISTENCE OF A BOUNDED INVARIANT REGION FOR COMPRESSIBLE EULER EQUATIONS IN DIFFERENT GAS STATES[J].Acta mathematica scientia,Series B, 2020, 40(5): 1229-1239.

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References 17

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THE EXISTENCE OF A BOUNDED INVARIANT REGION FOR COMPRESSIBLE EULER EQUATIONS IN DIFFERENT GAS STATES

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