三维可压缩 MHD 方程大解的时间衰减率

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1397-1408.

三维可压缩 MHD 方程大解的时间衰减率

陈菲^1,^*(),王帅¹(),赵永叶²(),王传宝¹()

¹青岛大学数学与统计学院山东青岛 266071
²广州航海学院广州 510725

收稿日期:2022-08-15 修回日期:2023-04-10 出版日期:2023-10-26 发布日期:2023-08-09
通讯作者: 陈菲 E-mail:feichenstudy@163.com;shuai172021@163.com;yongyezhao@163.com;wcb1216@163.com
作者简介:王帅，Email: shuai172021@163.com;|赵永叶，Email: yongyezhao@163.com;|王传宝，Email: wcb1216@163.com
基金资助:
国家自然科学基金(12101345);山东省自然科学基金(ZR2021QA017);广州市基础研究计划基础与应用基础研究项目(202102020283)

Time Decay Rate for Large-Solution About 3D Compressible MHD Equations

Chen Fei^1,^*(),Wang Shuai¹(),Zhao Yongye²(),Wang Chuanbao¹()

¹School of Mathematics and Statistics, Qingdao University, Shandong Qingdao 266071
²Department of Basic Courses, Guangzhou Maritime University, Guangzhou 510725

Received:2022-08-15 Revised:2023-04-10 Online:2023-10-26 Published:2023-08-09
Contact: Fei Chen E-mail:feichenstudy@163.com;shuai172021@163.com;yongyezhao@163.com;wcb1216@163.com
Supported by:
NSFC(12101345);Natural Science Foundation of Shandong Province of China(ZR2021QA017);Basic and Applied Basic Research Project of Guangzhou Basic Research Plan(202102020283)

摘要/Abstract

摘要：

该文主要研究 $\mathbb{R}^3$ 中可压缩磁流体力学方程大解的时间衰减率. 当 $(\sigma_{0}-1,u_{0},M_{0})$ 属于 $L^1\cap H^2$ 时, 基于 Chen[1] 等人的成果, 文献 [2] 中得到了 $\|\nabla(\sigma-1,u,M)\|_{H^1}\leqslant C(1+t)^{-\frac{5}{4}}$, 可见, 解二阶导数的时间衰减率不是最理想的. 因此, 该文通过借助频率分解[3] 的方法将 $\|\nabla^2 (\sigma-1,u,M)\|_{L^2}$ 的时间衰减率改进为 $(1+t)^{-\frac{7}{4}}$.

关键词: 时间衰减率, 大解, 可压缩磁流体力学方程

Abstract:

This paper focus on time decay rate for large-solution about compressible magnetohydrodynamic equations in $\mathbb{R}^3$. Provided that $(\sigma_{0}-1,u_{0},M_{0})\in L^1\cap H^2$, based on the work of Chen et al.[1], $\|\nabla(\sigma-1,u,M)\|_{H^1}\leqslant C(1+t)^{-\frac{5}{4}}$ is obtained in reference [2], obviously, time decay rate of the 2nd-order derivative of the solution in [2] is not ideal. Here, we improve that of $\|\nabla^2 (\sigma-1,u,M)\|_{L^2}$ to be $(1+t)^{-\frac{7}{4}}$ by the frequency decomposition method[3].

Key words: Time decay rate, Large-solution, Compressible magnetohydrodynamic equations

中图分类号:

O175

陈菲,王帅,赵永叶,王传宝. 三维可压缩 MHD 方程大解的时间衰减率[J]. 数学物理学报, 2023, 43(5): 1397-1408.

Chen Fei,Wang Shuai,Zhao Yongye,Wang Chuanbao. Time Decay Rate for Large-Solution About 3D Compressible MHD Equations[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1397-1408.

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