| Abstract: |
| In this talk, we consider the Cauchy problem for both the resistive and non-resistive magnetohydrodynamics (MHD) equations in the one-dimensional space. Based on the full use of effective viscous flux and the Caffarelli-Kohn-Nirenberg weighted inequality, we established the global existence and uniqueness of strong solutions for large initial data and vacuum when the viscosity coefficient is assumed to be constant or density-dependent. Besides, the non-resistive limit of global solutions with large data is also justified. |
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