Large-Time Existence and Decay of Entropy Solutions for Unsteady Isentropic Gas Flow in the Quasi-One-Dimensional Nozzle

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-09-05 DOI:10.1111/sapm.70104

Jianjun Chen, Qiquan Fang, Yun-guang Lu, Naoki Tsuge

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引用次数: 0

Abstract

In this paper, we apply the viscosity–flux approximation method coupled with the maximum principle to obtain the a priori $L^{\infty}$ estimates for the viscosity approximation solutions of the unsteady isentropic gas flow in the de Laval nozzle. Then by applying the compensated compactness method, we obtain the global existence of entropy solutions. Finally, we study the large-time behavior of solutions and show the decay of the $L^{γ}$ norm of density for any adiabatic exponent $γ > 1$ .

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准一维喷管中非定常等熵气体流动熵解的大时间存在性和衰减性

本文应用黏度-通量近似法结合极大值原理，得到了de Laval喷嘴内非定常等熵气体流动黏度近似解的先验L∞$L^{\infty }$估计。然后应用补偿紧性方法，得到了熵解的全局存在性。最后，我们研究了解的大时间行为，并证明了任意绝热指数γ ＆gt； 1 $\gamma >1$的L γ $L^{\gamma }$密度范数的衰减。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.