双曲型普朗特方程在 Gevrey 空间中的长时间适定性——献给陈化教授 70 寿辰

数学物理学报 ›› 2026, Vol. 46 ›› Issue (2): 616-627.

双曲型普朗特方程在 Gevrey 空间中的长时间适定性——献给陈化教授 70 寿辰

李维喜^*(), 王佳希(), 徐展()

武汉大学数学与统计学院武汉 430072

收稿日期:2025-12-22 修回日期:2026-01-27 出版日期:2026-04-26 发布日期:2026-04-27
通讯作者: 李维喜 E-mail:wei-xi.li@whu.edu.cn;wangjiaxi@whu.edu.cn;xuzhan@whu.edu.cn
作者简介:王佳希, Email：wangjiaxi@whu.edu.cn
徐展, Email：xuzhan@whu.edu.cn
基金资助:
国家自然科学基金(12325108);国家自然科学基金(12131017);国家自然科学基金(12221001);湖北省计算数学重点实验室(2019CFA007)

Long-Time Well-Posedness of the Hyperbolic Prandtl Equations in Gevrey Spaces

Weixi Li^*(), Jiaxi Wang(), Zhan Xu()

School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received:2025-12-22 Revised:2026-01-27 Online:2026-04-26 Published:2026-04-27
Contact: Weixi Li E-mail:wei-xi.li@whu.edu.cn;wangjiaxi@whu.edu.cn;xuzhan@whu.edu.cn
Supported by:
NSFC(12325108);NSFC(12131017);NSFC(12221001);Natural Science Foundation of Hubei Province(2019CFA007)

摘要/Abstract

摘要：

该文研究二维与三维双曲型普朗特方程在 Gevrey 空间中的长时间适定性. 作者证明: 该系统在 Gevrey 指标 $\leq 2$ 的 Gevrey 函数空间中, 对于小初值存在唯一的长时间解. 证明基于一种新的线性项相消机制以及半径关于时间的衰减速率.

关键词: 双曲型普朗特方程, Gevrey 空间, 长时间适定性

Abstract:

In this paper, we investigate the 2D and 3D hyperbolic Prandtl equations. We prove that this system has a unique long-time solution with small initial data in Gevrey function space with index up to 2. The proof is based on a new cancellation mechanism with linear terms and the decay rate of the radius with respect to time.

Key words: hyperbolic Prandtl equations, Gevrey spaces, long-time well-posedness

中图分类号:

O175.23

李维喜, 王佳希, 徐展. 双曲型普朗特方程在 Gevrey 空间中的长时间适定性——献给陈化教授 70 寿辰[J]. 数学物理学报, 2026, 46(2): 616-627.

Weixi Li, Jiaxi Wang, Zhan Xu. Long-Time Well-Posedness of the Hyperbolic Prandtl Equations in Gevrey Spaces[J]. Acta mathematica scientia,Series A, 2026, 46(2): 616-627.

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