Global well-posedness of 2D incompressible Magnetohydrodynamic equations with horizontal dissipation

<p style='text-indent:20px;'>This paper focuses on two-dimensional incompressible non-resistive MHD equations with only horizontal dissipation in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{T}\times\mathbb{R} $\end{document}</tex-math></inline-formula>. Invoking three Poincaré-type inequalities about the derivative, we study global well-posedness of system near a background magnetic via structure perturbation and symmetry condition imposed initial data. By precise time-weighted energy estimate, also establish damping. Here overcome difficulties brought by absence diffusion appearance boundary. We note that stability one-directional id="M2">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula> or bounded domain appears to be unknown.</p>