Global Stability of Multi-wave Configurations for the Compressible Non-isentropic Euler System

Min Ding

Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (6) : 921 -952.

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Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (6) : 921 -952. DOI: 10.1007/s11401-021-0298-x
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Global Stability of Multi-wave Configurations for the Compressible Non-isentropic Euler System

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Abstract

This paper is contributed to the structural stability of multi-wave configurations to Cauchy problem for the compressible non-isentropic Euler system with adiabatic exponent γ ∈ (1, 3]. Given some small BV perturbations of the initial state, the author employs a modified wave front tracking method, constructs a new Glimm functional, and proves its monotone decreasing based on the possible local wave interaction estimates, then establishes the global stability of the multi-wave configurations, consisting of a strong 1-shock wave, a strong 2-contact discontinuity, and a strong 3-shock wave, without restrictions on their strengths.

Keywords

Structural stability / Multi-wave configuration / Shock / Contact discontinuity / Compressible non-isentropic Euler system / Wave front tracking method

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Min Ding. Global Stability of Multi-wave Configurations for the Compressible Non-isentropic Euler System. Chinese Annals of Mathematics, Series B, 2021, 42(6): 921-952 DOI:10.1007/s11401-021-0298-x

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