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Analysis of non-isentropic compressible Euler equations with relaxation
Journal article   Open access   Peer reviewed

Analysis of non-isentropic compressible Euler equations with relaxation

Tong Li and Kun Zhao
Journal of Differential Equations, Vol.259(11), pp.6338-6367
12/05/2015
DOI: 10.1016/j.jde.2015.07.023
url
https://doi.org/10.1016/j.jde.2015.07.023View
Published (Version of record) Open Access

Abstract

This paper is contributed to the study of the one-dimensional non-isentropic compressible Euler equations with relaxation. It is shown that classical solutions do not exist globally-in-time under general conditions on initial data. Indeed, finite-time blowup occurs in a quantity related to the first moment. On the other hand, when the initial datum is sufficiently close to a constant equilibrium state, it is shown that the equations possess a unique global-in-time classical solution, and the solution converges to the equilibrium state in the long-time run. When the domain is finite, the convergence rate is shown to be exponential, due to boundary effects.
Finite-time blowup Global existence Long-time behavior Non-isentropic compressible Euler equations Relaxation

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