带阻尼的二维等熵可压缩欧拉方程组不稳定激波的生成

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2140-2166.

带阻尼的二维等熵可压缩欧拉方程组不稳定激波的生成

朱婉情^*()

南京师范大学数学科学学院 210023 南京, 金陵科技学院南京 211112

出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 朱婉情 E-mail:zwq15371032536@163.com
基金资助:
金陵科技学院博士科研启动基金(jit-b-202611)

The Unstable Shock Formation for 2D Isentropic Compressible Euler Equations with Damping

Wanqing Zhu^*()

School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, Department of Mathematics, Jinling Institute of Technology, 211112

Online:2026-12-26 Published:2026-08-14
Contact: Wanqing Zhu E-mail:zwq15371032536@163.com
Supported by:
PhD Research Start-up Fund of Jinling Institute of Technology(jit-b-202611)

摘要/Abstract

摘要：

文中主要考虑带阻尼的二维等熵可压缩欧拉方程组在角向对称条件下不稳定激波的生成问题. 对于阻尼欧拉方程组, 作者构造出不同于一般欧拉方程组的自相似坐标变换. 此外, 也选取该方程组的一类初值, 使它渐近收敛于阻尼 Burgers 方程的不稳定 $C^{{1}/{5}}$ 自相似解. 同时也引入调制变量技术和 Newton 迭代的方法来描述不稳定激波. 更进一步地, 爆破型在爆破时间具有 $C^{{1}/{5}}$ Hölder正则性的cusp奇性.

关键词: 可压缩欧拉方程组, 阻尼, 不稳定激波, 调制变量.

Abstract:

In this paper, we consider the unstable blowup mechanism for 2D isentropic compressible Euler equations with damping under azimuthal symmetry. We construct a suitable self-similar coordinate transformation for the damped Euler equations which is different from the general Euler equations. Besides, we also choose a kind of initial data which asymptotically converges to the unstable $C^{{1}/{5}}$ self-similar solution of the Burgers equation with damping. In addition, we introduce the modulation variables and the Newton iteration to describe the unstable shock. Further, the blowup profile has a cusp singularity of $C^{{1}/{5}}$ Hölder regularity at the blowup time.

Key words: compressible Euler equations, damping, unstable shock, modulation variables.

中图分类号:

O175.2

朱婉情. 带阻尼的二维等熵可压缩欧拉方程组不稳定激波的生成[J]. 数学物理学报, 2026, 46(6): 2140-2166.

Wanqing Zhu. The Unstable Shock Formation for 2D Isentropic Compressible Euler Equations with Damping[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2140-2166.

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