| Abstract: |
| This talk focuses on the compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in $\mathbb{R}^2$. We present a systematic approach to establish the global existence of smooth solutions when the initial data is close to a background magnetic field. To overcome key challenges arising from anisotropy and the critical nature of the system, we fully exploit the underlying dissipative structure and introduce several delicately constructed dissipative quantities. Compared with the previous works, we solve this problem by pure energy estimate without extra help from Sobolev spaces of negative index |
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