| Abstract: |
| In this talk, we consider the global existence results on the compressible and incompressible magnetohydrodynamics without magnetic diffusivity. The absence of dissipation in the magnetic field and density leads to significant analytical difficulties. To overcome this problem, we introduce the deformation gradient, which reveals an effective dissipative structure relating the magnetic field to the inverse deformation tensor. By developing time-weighted energy estimates, we establish the global well-posedness of classical solutions with small initial data around equilibrium |
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