Global Existence to Cauchy Problem for 1D Magnetohydrodynamics Equations

Magnetohydrodynamics are widely used in medicine and biotechnology, such as drug targeting, molecular biology, cell isolation and purification. In this paper, we prove the existence of a global strong solution to the one-dimensional compressible magnetohydrodynamics system with temperature-dependent...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-01, Vol.15 (1), p.80
Main Authors: Zhong, Jianxin, Xie, Xuejun
Format: Article
Language:English
Subjects:
Cauchy problem
Cauchy problems
Compressibility
compressible MHD equations
Fluid dynamics
Gases
global strong solution
Heat conductivity
Magnetic fields
Magnetohydrodynamics
Molecular biology
Temperature dependence
temperature-dependent heat conductivity
Thermal conductivity
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Summary:Magnetohydrodynamics are widely used in medicine and biotechnology, such as drug targeting, molecular biology, cell isolation and purification. In this paper, we prove the existence of a global strong solution to the one-dimensional compressible magnetohydrodynamics system with temperature-dependent heat conductivity in unbounded domains and a large initial value by the Lagrangian symmetry transformation, when the viscosity μ is constant and the heat conductivity κ, which depends on the temperature, satisfies κ=κ¯θb(b>1).
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15010080