| Abstract: |
| In this talk, we consider the stability of 3D Couette flow $(y,0,0)^\top$ in a uniform background magnetic field $\al(\sig, 0,1)^\top$. It is shown that if the background magnetic field $\al(\sig, 0,1)^\top$ with $\sig\in\mathbb{R}\backslash\mathbb{Q}$ satisfying a generic Diophantine condition is so strong that $|\al|\gg \fr{\nu+\mu}{\sqrt{\nu\mu}}$, and the initial perturbations $u_{\mathrm{in}}$ and $b_{\mathrm{in}}$ satisfy
$ \left\|(u_{\mathrm{in}},b_{\mathrm{in}})\right\|_{H^{N+2}}\ll\min\left\{\nu, \mu\right\}$ for sufficiently large $N$, then the resulting solution remains close to the steady state in $L^2$ at the same order for all time. Compared with the result of Liss [Comm. Math. Phys., 377(2020), 859--908], we use a more general energy method to address the physically relevant case $\nu\ne\mu$ based on some new observations. This is based on a joint work with Yulin Rao and Zhifei Zhang. |
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