Acta Mathematica Scientia

, Volume 39, Issue 2, pp 403–412 | Cite as

Time-Periodic Isentropic Supersonic Euler flows in One-Dimensional Ducts Driving by Periodic Boundary Conditions

  • Hairong YuanEmail author


We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.

Key words

supersonic flow isentropic compressible Euler equations duct time-periodic solution initial-boundary-value problem 

2010 MR Subject Classification

35B10 35L04 76G20 


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Mathematical Sciences; Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghaiChina

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