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December  2017, 10(4): 1035-1053. doi: 10.3934/krm.2017041

## Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vacuum

 1 Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China 2 School of Mathematics, Shandong University, Jinan 250100, China 3 Department of Mathematics, Nanjing University, Nanjing 210093, China

* S. Huang is the corresponding author

Received  September 2015 Revised  November 2016 Published  March 2017

This paper considers the initial boundary problem to the planar compressible magnetohydrodynamic equations with large initial data and vacuum. The global existence and uniqueness of large strong solutions are established when the heat conductivity coefficient
 $κ(θ)$
satisfies
 $C_{1}(1+\theta^q)\leq \kappa(\theta)\leq C_2(1+\theta^q)$
for some constants
 $q>0$
, and
 $C_1,C_2>0$
.
Citation: Jishan Fan, Shuxiang Huang, Fucai Li. Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vacuum. Kinetic & Related Models, 2017, 10 (4) : 1035-1053. doi: 10.3934/krm.2017041
##### References:

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