Existence, uniqueness and uniform stability of the solution for 3D incompressible MHD equations under the uniqueness condition

In this work, we present a uniqueness condition depending on (ν, μ, s, u0, B0, F) and consider the fully discrete Galerkin method for the 3D time-dependent incompressible MHD equations. Furthermore, we provide the global uniform well-posedness (or the existence, uniqueness and uniform stability of the solution) of the 3D time-dependent incompressible MHD equations under the uniqueness condition by use of the compact theorem and a new a priori estimate of the fully discrete Galerkin solution.