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 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).