Yong Zeng

Liouville-type theorems and perturbation uniqueness for stationary incompressible MHD with directional fractional dissipation

We study Liouville-type theorems for stationary solutions of the incompressible magnetohydrodynamics equations in $\mathbb{R}^n$, with directional fractional dissipation $(-\partial_i^2)^{\alpha}u$ and $(-\partial_j^2)^{\beta}b$, where $n\ge 2$ and $0<\alpha,\beta\le 1$. We prove that $u\equiv b\equiv 0$ by assuming th...