Temporal periodic solutions of non-isentropic compressible Euler equations with geometric effects

In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions a...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 13; no. 1; pp. 789 - 812
Main Authors Fang, Xixi, Ma, Shuyue, Yu, Huimin
Format Journal Article
LanguageEnglish
Published De Gruyter 27.11.2024
Subjects
35A01
35B10
35L50
geometric effects
non-isentropic compressible Euler equations
subsonic flow
temporal periodic solutions
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Summary:In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions around the steady states are proved by constructing a new iterative format technically. Besides, further regularity and stability of the obtained temporal periodic solutions are obtained, too. The main difficulty in the proof is coming from derivative loss, which is caused by the diagonalization. Observing that the entropy is conserved along the second characteristic curve, we overcome this difficulty by transforming the derivative of entropy with respect to into a derivative along the direction of first or third characteristic. The results demonstrate that dissipative boundary feedback control can stabilize the non-isentropic compressible Euler equations in qusi-one-dimensional nozzles.
ISSN:2191-950X
2191-950X
DOI:10.1515/anona-2024-0049