Abstract
Magnetohydrodynamics is concerned with the mutual interactions between moving, electrically conductive fluids and the magnetic field. It is widely applied in astrophysics, thermonuclear reactions and industry. The Cauchy problem to one-dimensional heat-conductive magnetohydrodynamic equations of viscous non-resistive gas is considered under the framework of Lagrangian coordinates. Based on the crucial upper and lower bounds of the density, we first obtain global well-posedness of strong solutions with regular initial data. Then existence of global weak solutions is established via the compactness analysis and the method of weak convergence. Stability of weak solutions is also verified by making full use of the specific mathematical structure of the equations. All results are obtained without any restriction to the size of the initial data.
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