(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
This paper is devoted to the study of the 3D incompressible magnetohydrodynamic system. We prove the local in time well-posedness for any large initial data in H^1_a,1(R^3) or H^1_a,1(R^3). Furthermore, the global well-posedness of a strong solution in L^∞(0, T; H^1_ a,1(R^3)) ∩ L^2 (0, T; H^1_a,1(R^3) ∩ H^2_a,1(R^3)) with initial data satisfying a smallness condition is established.