Global solution to the 2D non-dissipation MHD system with a velocity damping term

In this paper, we study the 2D non-dissipation MHD system with a velocity damping term in torus. To our knowledge, constructing the global solutions to this system is an important problem. Under the assumption that the initial data is small in \(H^{4}({\mathbb {T}}^{2})\) $H^4({\mathbb{T}}^2)$ , we establish the global well-posedness of the system.