| Abstract: |
| We study the global existence of classical solutions to the incompressible MHD system without magnetic diffusion in 2D and 3D. The lack of resistivity or magnetic diffusion poses a major challenge to a global regularity theory even for small smooth initial data. However, the interesting nonlinear structure of the system not only leads to some significant challenges, but some interesting stabilization properties. This helps the establishment of the global regularity and the existence of global strong solutions. |
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