三维可压缩磁流体力学方程组大解时间导数的衰减率
Decay Rates of Time Derivatives of Large Solutions of 3D Compressible Magnetohydrodynamics Equations
DOI: 10.12677/PM.2023.131003, PDF,    国家自然科学基金支持
作者: 孙彤彤, 陈 菲*：青岛大学数学与统计学院，山东 青岛
关键词: 可压缩磁流体力学方程组；大初值；衰减率；Compressible Magnetohydrodynamics Equations； Large Initial Data； Decay Rate
摘要: 本文主要研究三维等熵可压缩磁流体力学方程组大解(σ,u,B)的时间导数的大时间渐近行为。在大解本身及其一阶和二阶导数在L2中的衰减率分别为的基础上，本文证明了大解(σ,u,B)的时间导数的衰减率分别为。
Abstract: In this paper, we study the large time asymptotic behavior of the time derivatives of the large so-lutions (σ,u,B) for the 3D isentropic compressible magnetohydrodynamic system. On the basis of the decay rates of the large solutions and also their first order and second order spatial derivatives in L2 are respectivelywe prove that the decay rates of the time derivatives of the large solutions (σ,u,B) arerespectively.
文章引用：孙彤彤, 陈菲. 三维可压缩磁流体力学方程组大解时间导数的衰减率[J]. 理论数学, 2023, 13(1): 24-31. https://doi.org/10.12677/PM.2023.131003

参考文献

[1] He, L., Huang, J. and Wang, C. (2019) Global Stability of Large Solutions to the 3D Compressible Navier-Stokes Equations. Archive for Rational Mechanics and Analysis, 234, 1167-1222. [Google Scholar] [CrossRef] 
[2] Gao, J., Wei, Z. and Yao, Z. (2020) The Optimal Decay Rate of Strong Solution for the Compressible Navier-Stokes Equations with Large Initial Data. Physica D: Nonlinear Phenomena, 406, Article ID: 132506. [Google Scholar] [CrossRef] 
[3] Chen, Q. and Tan, Z. (2010) Global Existence and Convergence Rates of Smooth Solutions for the Compressible Magnetohydrodynamic Equations. Nonlinear Analysis: Theory, Methods & Applications, 72, 4438-4451. [Google Scholar] [CrossRef] 
[4] Li, F. and Yu, H. (2011) Optimal Decay Rate of Classical Solutions to the Compressible Magnetohydrodynamic Equations. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 141, 109-126. [Google Scholar] [CrossRef] 
[5] Zhang, J. and Zhao, J. (2010) Some Decay Estimates of Solu-tions for the 3-D Compressible Isentropic Magnetohydrodynamics. Communications in Mathematical Sciences, 8, 835-850. [Google Scholar] [CrossRef] 
[6] Gao, J., Chen, Y. and Yao, Z. (2015) Long-Time Be-havior of Solution to the Compressible Magnetohydrodynamic Equations. Nonlinear Analysis, 128, 122-135. [Google Scholar] [CrossRef] 
[7] Guo, Y. and Wang, Y. (2012) Decay of Dissipative Equations and Negative Sobolev Spaces. Communications in Partial Differential Equations, 37, 2165-2208. [Google Scholar] [CrossRef] 
[8] Tan, Z. and Wang, H. (2013) Optimal Decay Rates of the Compressible Magnetohydrodynamic Equations. Nonlinear Analysis: Real World Applications, 14, 188-201. [Google Scholar] [CrossRef] 
[9] Pu, X. and Guo, B. (2013) Global Existence and Convergence Rates of Smooth Solutions for the Full Compressible MHD Equations. Zeitschrift für Angewandte Mathematik und Physik, 64, 519-538. [Google Scholar] [CrossRef] 
[10] Gao, J., Tao, Q. and Yao, Z. (2016) Optimal Decay Rates of Classical Solutions for the Full Compressible MHD Equations. Zeitschrift für Angewandte Mathematik und Physik, 67, Article No. 23. [Google Scholar] [CrossRef] 
[11] Gao, J. and Yao, Z.-A. (2015) Global Existence and Optimal Decay Rates of Solutions for Compressible Hall-MHD Equations. Discrete and Continuous Dynamical Systems, 36, 3077-3106. [Google Scholar] [CrossRef] 
[12] Chen, Y., Huang, J. and Xu, H. (2019) Global Stabil-ity of Large Solutions of the 3-D Compressible Magnetohydrodynamic Equations. Nonlinear Analysis: Real World Ap-plications, 47, 272-290. [Google Scholar] [CrossRef] 
[13] Gao, J., Wei, Z. and Yao, Z. (2020) Decay Rate of Strong So-lution for the Compressible Magnetohydrodynamic Equations with Large Initial Data. Applied Mathematics Letters, 102, Article ID: 106100. [Google Scholar] [CrossRef] 
[14] Wang, S., Chen, F., Zhao, Y. and Wang, C. (2022) Estimation of Decay Rates to Large-Solutions of 3D Compressible Magnetohydrodynamic System. Journal of Mathematical Physics, 63, Article ID: 111507. [Google Scholar] [CrossRef] 
[15] Wang, S., Chen, F. and Wang, C. (2022) Optimal Time Decay Estimation for Large-Solution about 3D Compressible MHD Equations. ArXiv Preprint ArXiv: 2206.05117.
[16] Adams, R.A. (1975) Sobolev Spaces. Academic Press, New York, 975 p.
[17] Deckelnick, K. (1992) Decay Estimates for the Compressible Navier-Stokes Equations in Unbounded Domains. Mathematische Zeitschrift, 209, 115-130. [Google Scholar] [CrossRef] 

为你推荐