Global Strong Solutions to the Cauchy Problem of 2D Nonhomogeneous Magnetohydrodynamic Equations With Density‐Dependent Viscosity and Resistivity

This paper is concerned with the global well‐posedness of strong solutions to the Cauchy problem for the modified two‐dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density‐dependent viscosity and resistivity, where the far‐field density could be either vacuum or nonvacuum. Notably, the initial data can be arbitrarily large and the initial density is allowed to vanish. Furthermore, the large‐time asymptotic behavior of the gradients of the velocity, the magnetic and the pressure is also established.