Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain

Jishan Fan; Fucai Li; Gen Nakamura

doi:10.3934/proc.2015.0387

Article Contents

2015, Volume 2015: 387-394. Doi: 10.3934/proc.2015.0387 open access

This issue Previous Article Steiner symmetrization for concave semilinear elliptic and parabolic equations and the obstacle problem Next Article A regularity criterion for 3D density-dependent MHD system with zero viscosity

Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain

1.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037
2.
Department of Mathematics, Nanjing University, Nanjing 210093
3.
Department of Mathematics, Inha University, Incheon 402-751

Received: July 2014

Revised: January 2015

Published: October 2015

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Abstract

In this paper we establish the global existence of strong solutions to the three-dimensional compressible magnetohydrodynamic equations in a bounded domain with small initial data. Moreover, we study the low Mach number limit to the corresponding problem.

Keywords:

Compressible magnetohydrodynamic equations,
global existence,
low Mach number limit.

Mathematics Subject Classification: Primary: 76W05; Secondary: 35B40.

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References

[1]	Q. Chen, Z. Tan, Global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamic equations, Nonlinear Anal. 72(2010) 4438-4451.
[2]	C. Dou, S. Jiang and Q. Ju, Global existence and the low Mach number limit for the compressible magnetohydrodynamic equations in a bounded domain with perfectly conducting boundary, Z. Angew. Math. Phys. 64(6)(2013) 1661-1678.
[3]	C. Dou, Q. Ju, Low Mach number limit for the compressible magnetohydrodynamic equations in a bounded domain for all time, Commun. Math. Sci. 12(4)(2014) 661-679.
[4]	B. Ducomet, E. Feireisl, The equations of magnetohydrodynamics: On the interaction between matter and radiation in the evolution of gaseous stars, Commun. Math. Phys. 266(2006) 595-629.
[5]	J. Fan, W. Yu, Strong solution to the compressible magnetohydrodynamic equations with vacuum, Nonlinear Anal.: RWA 10(2009) 392-409.
[6]	J. Fan, W. Yu, Global variational solutions to the compressible magnetohydrodynamic equations, Nonlinear Anal. 69(2008) 3637-3660.
[7]	J. Fan, H. Gao and B. Guo, Low Mach number limit of the compressible magnetohydrodynamic equations with zero thermal conductivity coefficient, Math. Methods Appl. Sci. 34 (2011) 2181-2188.
[8]	X. Hu, D. Wang, Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows, Arch. Ration. Mech. Anal. 197(2010) 203-238.
[9]	X. Hu, D. Wang, Global solutions to the three-dimensional full compressible magnetohydrodynamic flow, Commun. Math. Phys. 283(2008) 255-284.
[10]	X. Hu, D. Wang, Low Mach number limit of viscous compressible magnetohydrodynamic flows, SIAM J. Math. Anal. 41(2009) 1272-1294.
[11]	S. Jiang, Q. Ju and F. Li, Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions, Commun. Math. Phys. 297(2010) 371-400.
[12]	S. Jiang, Q. Ju and F. Li, Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients, SIAM J. Math. Anal. 42 (2010), 2539-2553.
[13]	S. Jiang, Q. Ju, F. Li, Low Mach number limit for the multi-dimensional full magnetohydrodynamic equations, Nonlinearity 25 (2012), no. 5, 1351-1365.
[14]	S. Jiang, Q. Ju, F. Li and Z. Xin, Low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data, Adv. Math. 259 (2014), 384-420.
[15]	F. Li, H. Yu, Optimal decay rate of classical solutions to the compressible magnetohydrodynamic equations, Proc. Royal Soc. Edinburgh 141A(2011) 109-126.
[16]	A. Suen, D. Hoff, Global low-energy weak solutions of the equations of three-dimensional compressible magnetohydrodynamics, Arch. Ration. Mech. Anal. 205 (2012), no. 1, 27-58.
[17]	A. I. Vol'pert, S. I. Hudjaev, On the Cauchy problem for composite systems of nonlinear differential equations, Math. USSR.-Sb. 16(1972) 517-544.
[18]	Y. Yang, X. Gu and C. Dou, Global well-posedness of strong solutions to the magnetohydrodynamic equations of compressible flows, Nonlinear Anal. 95 (2014), 23-37.