| Abstract: |
| This talk is concerned with the stability theory of n-dimensional incompressible and compressible magnetohydrodynamic ({\it MHD for short}) equations with only kinematic viscosity or magnetic diffusion in the periodic domain {{\mathbb{T}}^n}. I will present some new results on the asymptotic stability and sharp decay estimates of this system when the magnetic field close to an equilibrium state satisfying the Diophantine condition. In the present works, by exploiting and effectively utilizing the structure of perturbation system, a new dissipative mechanism is found out and applied so that we can sharply improve the spaces of existing works, where the decay estimates and asymptotic stability of solutions are taking place. Some key ideas of our method will be discussed. This talk is based on joint works with Quansen Jiu and Yaowei Xie. |
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