The Cauchy problem for the 2D magnetohydrodynamic-αα equations

In this paper, we consider the Cauchy problem for the 2D incompressible magnetohydrodynamics-αα (MHD-αα) equations. We obtain the global solution for the 2D incompressible MHD-αα simulation model in the fractional index Sobolev space, and prove that the incompressible MHD-αα equations reduce to the incompressible homogeneous MHD equations as α→0α→0, and the solution of MHD-αα equations will converge to the weak solution of the corresponding MHD equations. Moreover, it is convenient to construct a numerical algorithm based on an iteration scheme in our proof.