TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS

doi:10.1007/s10473-019-0206-6

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 403-412.doi: 10.1007/s10473-019-0206-6

TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS

袁海荣

School of Mathematical Sciences;Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai 200241, China

收稿日期:2018-03-07 修回日期:2018-11-04 出版日期:2019-04-25 发布日期:2019-05-06
作者简介:Hairong YUAN,hryuan@math.ecnu.edu.cn
基金资助:
The author was supported by the National Natural Science Foundation of China (11371141 and 11871218); Science and Technology Commission of Shanghai Municipality (STCSM) under Grant No. 18dz2271000.

TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS

Hairong YUAN

School of Mathematical Sciences;Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai 200241, China

Received:2018-03-07 Revised:2018-11-04 Online:2019-04-25 Published:2019-05-06
Supported by:
The author was supported by the National Natural Science Foundation of China (11371141 and 11871218); Science and Technology Commission of Shanghai Municipality (STCSM) under Grant No. 18dz2271000.

摘要/Abstract

摘要： 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.

关键词: supersonic flow, isentropic, compressible Euler equations, duct, time-periodic solution, initial-boundary-value problem

Abstract: 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

袁海荣. TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2019, 39(2): 403-412.

Hairong YUAN. TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS[J]. Acta mathematica scientia,Series B, 2019, 39(2): 403-412.

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TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS

TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS

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