球对称非等熵可压缩 Navier-Stokes 方程的自由边界问题——献给邓引斌教授 70 寿辰

数学物理学报 ›› 2026, Vol. 46 ›› Issue (4): 1374-1392.

球对称非等熵可压缩 Navier-Stokes 方程的自由边界问题——献给邓引斌教授 70 寿辰

董文超¹^,²(), 郭真华¹^,²^,^*(), 李振甲¹^,²()

¹ 广西大学数学学院南宁 530004
² 广西应用数学中心 (广西大学) 南宁 530004

收稿日期:2025-12-19 修回日期:2026-04-30 出版日期:2026-08-26 发布日期:2026-06-10
通讯作者: 郭真华 E-mail:wcdong@gxu.edu.cn;zhguo@gxu.edu.cn;1467663039@qq.com
作者简介:董文超,E-mail: wcdong@gxu.edu.cn;
李振甲, E-mail: 1467663039@qq.com
基金资助:
国家自然科学基金(12501298);国家自然科学基金(11931013);广西自然科学基金(2026GXNSFBA00640111);广西自然科学基金(2022GXNSFDA035078)

Free Boundary Problem for the Spherically Symmetric Non-Isentropic Compressible Navier-Stokes Equations

Wenchao Dong¹^,²(), Zhenhua Guo¹^,²^,^*(), Zhenjia Li¹^,²()

¹ School of Mathematics, Guangxi University, Nanning 530004
² Center for Applied Mathematics of Guangxi (Guangxi University), Nanning 530004

Received:2025-12-19 Revised:2026-04-30 Online:2026-08-26 Published:2026-06-10
Contact: Zhenhua Guo E-mail:wcdong@gxu.edu.cn;zhguo@gxu.edu.cn;1467663039@qq.com
Supported by:
NSFC(12501298);NSFC(11931013);GXNSF(2026GXNSFBA00640111);GXNSF(2022GXNSFDA035078)

摘要/Abstract

摘要：

关于输运系数依赖于温度的非等熵可压缩 Navier-Stokes 方程大初值全局适定性问题的研究, 目前主要集中于一维情形, 高维情形的结果相对较少. 针对黏性系数为常数、热传导系数依赖于温度和密度的三维球对称非等熵可压缩 Navier-Stokes 方程的自由边界问题, 在初值属于 $H^1$-空间的条件下, 建立了全局强解的存在唯一性.

关键词: 球对称 Navier-Stokes 方程, 自由边界问题, 适定性

Abstract:

Research on the global well-posedness for the non-isentropic compressible Navier-Stokes equations with large initial data, where the transport coefficients depend on temperature, has primarily focused on the one-dimensional case, while results in higher dimensions remain relatively scarce. This paper studies a free boundary problem for the three-dimensional spherically symmetric non-isentropic compressible Navier-Stokes equations, assuming constant viscosity and heat conductivity depending on both temperature and density. Under the condition that the initial data belong to the $H^1$ space, we establish the existence and uniqueness of global strong solution.

Key words: spherically symmetric Navier-Stokes equations, free boundary problem, well-posedness

中图分类号:

O175.2

董文超, 郭真华, 李振甲. 球对称非等熵可压缩 Navier-Stokes 方程的自由边界问题——献给邓引斌教授 70 寿辰[J]. 数学物理学报, 2026, 46(4): 1374-1392.

Wenchao Dong, Zhenhua Guo, Zhenjia Li. Free Boundary Problem for the Spherically Symmetric Non-Isentropic Compressible Navier-Stokes Equations[J]. Acta mathematica scientia,Series A, 2026, 46(4): 1374-1392.

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