二维可压缩Prandtl方程倒流点的存在性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 691-701.

二维可压缩Prandtl方程倒流点的存在性

邹永辉(),徐鑫^*()

中国海洋大学数学科学学院山东青岛 266100

收稿日期:2022-09-27 修回日期:2022-11-28 出版日期:2023-06-26 发布日期:2023-06-01
通讯作者: 徐鑫 E-mail:zouyonghuimath@163.com;xx@ouc.edu.cn
作者简介:邹永辉, E-mail: zouyonghuimath@163.com
基金资助:
国家自然科学基金(12001506)

Existence of Back-Flow Point for the Two-Dimensional Compressible Prandtl Equation

Zou Yonghui(),Xu Xin^*()

School of Mathematical Sciences, Ocean University of China, Shandong Qingdao 266100

Received:2022-09-27 Revised:2022-11-28 Online:2023-06-26 Published:2023-06-01
Contact: Xin Xu E-mail:zouyonghuimath@163.com;xx@ouc.edu.cn
Supported by:
NSFC(12001506)

摘要/Abstract

摘要：

该文研究了二维非稳态可压缩Prandtl边界层方程倒流点的存在性, 在Oleinik单调性假设下, 作者首先利用极值原理得到了第一个倒流点如果出现, 那么一定出现在边界$\left\{y=0\right\}$上. 其次, 当压力满足一致逆压梯度条件并且初始值满足一定增长条件时, 作者通过Lyapunov泛函方法得到倒流点的存在性. 最后给出倒流点存在的实例.

关键词: 可压缩Prandtl方程, 倒流点, 极值原理, 逆压梯度, Lyapunov泛函

Abstract:

In this paper, we study the back-flow problem of the two-dimensional unsteady compressible Prandtl boundary layer equations. By using the maximum principle, we obtain that a first back-flow point should appear on the boundary $\left\{y=0\right\}$ if back-flow occurs under Oleinik's monotonicity assumption. Moreover, when the pressure gradient of the outer flow is adverse and the initial velocity satisfies certain growth condition, we obtain the existence of a back-flow point of the compressible Prandtl boundary layer by Lyapunov functional method. Finally, an example of the existence of the back-flow point is given.

Key words: Compressible Prandtl equation, Back-flow point, The maximum principle, Adverse pressure gradient, Lyapunov functional

中图分类号:

O175.29

邹永辉,徐鑫. 二维可压缩Prandtl方程倒流点的存在性[J]. 数学物理学报, 2023, 43(3): 691-701.

Zou Yonghui,Xu Xin. Existence of Back-Flow Point for the Two-Dimensional Compressible Prandtl Equation[J]. Acta mathematica scientia,Series A, 2023, 43(3): 691-701.

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