倾斜薄膜流圣韦南方程非单调水力冲击的存在性和稳定性

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-09-13 DOI:10.1007/s00205-024-02033-4

Grégory Faye, L. Miguel Rodrigues, Zhao Yang, Kevin Zumbrun

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引用次数: 0

摘要

通过扩展杨-仲布伦（Yang-Zumbrun）针对弗劳德数（F<2\）的流体力学稳定情况所做的工作，我们对倾斜薄膜流的圣维南方程的水力冲击剖面的存在性和对流稳定性进行了完整的分类。此外，我们还通过数值实验证实，一般黎曼数据的渐近动力学在流体力学不稳定性机制下，要么是稳定的水力冲击波，要么是由入侵的滚动波浪前沿组成的模式，该波浪前沿被一个有限的终止拉克斯冲击从正无穷处的恒定状态分隔开来。值得注意的是，剖面图、存在图和稳定图都是通过数学分析和显式计算严格获得的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Existence and Stability of Nonmonotone Hydraulic Shocks for the Saint Venant Equations of Inclined Thin-Film Flow

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Existence and Stability of Nonmonotone Hydraulic Shocks for the Saint Venant Equations of Inclined Thin-Film Flow

Extending the work of Yang–Zumbrun for the hydrodynamically stable case of Froude number \(F<2\), we categorize completely the existence and convective stability of hydraulic shock profiles of the Saint Venant equations of inclined thin film flow. Moreover, we confirm by numerical experiment that asymptotic dynamics for general Riemann data is given in the hydrodynamic instability regime by either stable hydraulic shock waves, or a pattern consisting of an invading roll wave front separated by a finite terminating Lax shock from a constant state at plus infinity. Notably, profiles, and existence and stability diagrams, are all rigorously obtained by mathematical analysis and explicit calculation.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.