Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Local strong solutions to the compressible viscous magnetohydrodynamic equations

Pages: 1617 - 1633, Volume 21, Issue 5, July 2016      doi:10.3934/dcdsb.2016014

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Tong Tang - Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098, China (email)
Hongjun Gao - Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China (email)

Abstract: In this paper, we consider the compressible magnetohydrodynamic equations with nonnegative thermal conductivity and electric conductivity. The coefficients of the viscosity, heat conductivity and magnetic diffusivity depend on density and temperature. Inspired by the framework of [11], [13] and [15], we use the maximal regularity and contraction mapping argument to prove the existence and uniqueness of local strong solutions with positive initial density in the bounded domain for any dimension.

Keywords:  Existence, strong solutions, compressible magnetohydrodynamic.
Mathematics Subject Classification:  Primary: 35Q35, 76W05, 76N10.

Received: January 2014;      Revised: March 2014;      Available Online: April 2016.