• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1521-1537
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• 2021

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in ℝ^d with d ≥ 2, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then the compressible magnetohydrodynamic system has a unique global solution. Our result improves the previous one by Danchin and Mucha [10] who considered the compressible Navier-Stokes equations.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.1
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• pp.86.1-86.1
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• 2011

Most astrophysical systems are turbulent and magnetized. Magnetic field plays an important role in the dynamics of ISM and influence all of properties of astrophysical system. Information of magnetic field is very important to understand properties of astrophysical systems. For example, one way to obtain information of magnetic field is to use Rotation Measure. Mean strength of the magnetic field along the line of sight can be estimated from RM/DM. (where RM is rotation measure, DM is dispersion measure) For the estimation of magnetic field strength using RM/DM, the correlation between density and magnetic field is very important. When there is no correlation between density and magnetic field the relation gives exact mean magnetic field strength. But, if the correlation is positive, it overestimates the magnetic field strength, while if the correlation is negative, it underestimate the strength. We calculate correlation between density and magnetic field in compressible MHD turbulence.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.107.2-107.2
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• 2011

Most astrophysical systems are turbulent and magnetized. Magnetic field plays an important role in the dynamics of astrophysical system and influence all of properties of astrophysical system. Therefore, information of magnetic field is very important to understand properties of astrophysical system. One way to obtain information of magnetic field is to use rotation measure. Mean strength of the magnetic field along the line of sight can be estimated from RM/DM, where RM is rotation measure and DM is dispersion measure. For the estimation of magnetic field strength using RM/DM, the correlation between density and magnetic field. When there is no correlation between density and magnetic field the relation gives exact mean magnetic strength. But if the positive correlation, it overestimates the magnetic field strength, while if the correlation is negative, it underestimate the magnetic field strength. In general, the ICM (intracluter medium) and the ISM (interstellar medium) cases, viscosity has a value greater than magnetic diffusion. We performed compressible MHD turbulence simulations and we studied correlation between density and magnetic field in different values of viscosity and magnetic diffusion. In most cases, we found weak or negative relations between the density and magnetic fields. We discuss implication of our results.