有界域中三维可压缩磁流体系统大初值强解的整体适定性

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 215-237.

有界域中三维可压缩磁流体系统大初值强解的整体适定性

张明玉()

潍坊学院数学与统计学院山东潍坊 261061

收稿日期:2025-03-31 修回日期:2025-07-08 出版日期:2026-02-26 发布日期:2026-01-19
作者简介:张明玉, Email: wfumath@126.com
基金资助:
山东省自然科学基金(ZR2024MA033)

Global Well-Posedness of Strong Solutions to Compressible Magnetohydrodynamic System with Large Initial Data in 3D Bounded Domains

Mingyu Zhang()

School of Mathematics and Statistics, Weifang University, Shandong Weifang 261061

Received:2025-03-31 Revised:2025-07-08 Online:2026-02-26 Published:2026-01-19
Supported by:
Natural Science Foundation of Shandong Province(ZR2024MA033)

摘要/Abstract

摘要：

研究了三维有界矩形域中可压缩磁流体力学系统, 该系统的速度场满足滑移边界条件, 磁场满足完全导电条件. 对于具有大能量的正则性初值, 证明了该初边值问题全局强解的存在唯一性.

关键词: 可压缩磁流体力学系统, 全局强解, 唯一性, 大初值

Abstract:

The three-dimensional (3D) compressible magnetohydrodynamic system is studied in a bounded rectangular domain with slip boundary condition for the velocity field and perfect conduction for the magnetic field. For the regular initial data with large energy, the global well-posedness of strong solutions to the initial-boundary-value problem of this system is obtained.

Key words: compressible magnetohydrodynamic system, global strong solutions, uniqueness, large initial data

中图分类号:

O175.2

张明玉. 有界域中三维可压缩磁流体系统大初值强解的整体适定性[J]. 数学物理学报, 2026, 46(1): 215-237.

Mingyu Zhang. Global Well-Posedness of Strong Solutions to Compressible Magnetohydrodynamic System with Large Initial Data in 3D Bounded Domains[J]. Acta mathematica scientia,Series A, 2026, 46(1): 215-237.

参考文献 32

[1]	Agmon S, Douglis A, Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations I. Commun Pure Appl Math, 1959, 12: 623-727 doi: 10.1002/cpa.v12:4
[2]	Bendali A, Domíngue J M, Gallic S. A variational approach for the vector potential formulation of the Stokes and Navier-Stokes problem in three-dimensional domains. J Math Anal Appl, 1985, 107(2): 537-560 doi: 10.1016/0022-247X(85)90330-0
[3]	Bella P, Feireisl E, Jin B J. Robustness of strong solutions to the compressible Navier-Stokes system. Math Ann, 2015, 362: 281-303 doi: 10.1007/s00208-014-1119-2
[4]	Cabannes H. Theoretical Magnetofluiddynamics. New York: Academic Press, 1970
[5]	Chen G Q, Wang D H. Global solution of nonlinear magnetohydrodynamics with large initial data. J Differential Equations, 2002, 182: 344-376 doi: 10.1006/jdeq.2001.4111
[6]	Chen G Q, Wang D H. Existence and continuous dependence of large solutions for the magnetohydrodynamic equations. Z Angew Math Phys, 2023, 54: 608-632 doi: 10.1007/s00033-003-1017-z
[7]	Cho Y, Choe H J, Kim H. Unique solvability of the initial boundary value problems for compressible viscous fluid. J Math Pures Appl, 2004, 83: 243-275 doi: 10.1016/j.matpur.2003.11.004
[8]	Ducomet B, Feireisl E. The equations of magnetohydrodynamics: On the interaction between matter and radiation in the evolution of gaseous stars. Commun Math Phys, 2006, 266: 595-629 doi: 10.1007/s00220-006-0052-y
[9]	Fan J S, Jiang S, Nakamura G. Vanishing shear viscosity limit in the magnetohydrodynamic equations. Commun Math Phys, 2007, 270: 691-708 doi: 10.1007/s00220-006-0167-1
[10]	Fan J S, Yu W. Global variational solutions to the compressible magnetohydrodynamic equations. Nonlinear Anal, 2008, 69: 3637-3660 doi: 10.1016/j.na.2007.10.005
[11]	Fan J S, Yu W. Strong solutions to the compressible MHD equations with vacuum. Nonlinear Anal. Real World Appl, 2009, 10: 392-409 doi: 10.1016/j.nonrwa.2007.10.001
[12]	Hoff D. Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data. J Differ Eqs, 1995, 120(1): 215-254 doi: 10.1006/jdeq.1995.1111
[13]	Hoff D. Local solutions of a compressible flow problem with Navier boundary conditions in general three-dimensional domains. SIAM Math Anal, 2012, 44(2): 633-650 doi: 10.1137/110827065
[14]	Huang X D, Li J, Xin Z P. Global well-posedness of strong solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations. Comm Pure Appl Math, 2012, 65: 549-585 doi: 10.1002/cpa.v65.4
[15]	Hu X, Wang D. Global solutions to the three-dimensional full compressible magnetohydrodynamic flows. Commun Math Phys, 2008, 283: 255-284 doi: 10.1007/s00220-008-0497-2
[16]	Hu X, Wang D. Compactness of weak solutions to the three-dimensional compressible magnetohydrodynamic equations. J Differential Equations, 2008, 245: 2176-2198 doi: 10.1016/j.jde.2008.07.019
[17]	Hu X, Wang D. Low mach number limit of viscous compressible magnetohydrodynamic flows. SIAM J Math Anal, 2009, 41: 127-1294
[18]	Hu X, Wang D. Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows. Arch Ration Mech Anal, 2010, 197: 203-238 doi: 10.1007/s00205-010-0295-9
[19]	Jiang S, Ju Q G, Li F C. Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. Commun Math Phys, 2010, 297: 371-400 doi: 10.1007/s00220-010-0992-0
[20]	Kawashima S, Okada M. Smooth global solutions for the one-dimensional equations in magnetohydrodynamics. Proc Japan Acad Ser A Math Sci, 1982, 58: 384-387
[21]	Kawashima S, Shizuta Y. Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid. Tsukuba J Math, 1986, 10: 131-149
[22]	Kawashima S. Smooth global solutions for two-dimensional equations of electromagneto-fluid dynamics. Japan J Appl Math, 1984, 1: 207-222 doi: 10.1007/BF03167869
[23]	Kawashima S, Shizuta Y. Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid II. Proc Japan Acad, 1986, 62: 181-184 doi: 10.2183/pjab.62.181
[24]	Kulikovskiy A F, Lyubimov G A. Magnetohydrodynamics. MA: Addison-Wesley Reading, 1965
[25]	Ladyzenskaja O A, Solonnikov V A, Ural'ceva N N. Linear and Quasilinear Equations of Parabolic Type. Providence, RI: American Mathematical Society, 1968
[26]	Li H L, Xu X Y, Zhang J W. Global strong solutions to 3D compressible magnetohydrodynamic equations with large oscillations and vacuum. SIAM J Math Anal, 2013, 45: 1356-1387 doi: 10.1137/120893355
[27]	Umeda T, Kawashima S, Shizuta Y. On the decay of solutions to the linearized equations of electromagnetofluid dynamics. Japan J Appl Math, 1984, 1(2): 435-457 doi: 10.1007/BF03167068
[28]	Vol'pert A I, Khudiaev S I. On the Cauchy problem for composite systems of nonlinear equations. Mat Sb, 1972, 29(4): 504-528
[29]	Wang D H. Large solutions to the initial-boundary problem for planar magnetohydrodynamics. SIAM J Appl Math, 2003, 63(4): 1424-1441 doi: 10.1137/S0036139902409284
[30]	Zhang J W, Jiang S, Xie F. Global weak solutions of an initial boundary problem for screw pinches in plasma physics. Math Models Methods Appl Sci, 2009, 19(6): 833-875 doi: 10.1142/S0218202509003644
[31]	Zhang J W, Zhao J N. Some decay estimates of solutions for the 3-D compressible isentropic magnetohydrodynamics. Commun Math Sci, 2010, 8: 835-850 doi: 10.4310/CMS.2010.v8.n4.a2
[32]	Zlotinik A A. Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations. Diff Equations, 2000, 36(5): 701-716