Magneto hydrodynamics (MHD) is the study of the interaction between magnetic fields and moving conducting fluids. The simplest example of an electrically conducting fluid is a liquid metal like mercury or liquid sodium. The equations describing the motion of a viscous incompressible conducting fluid moving in a magnetic field are derived by coupling Navier-Stokes equations with Maxwell’s equations together with expression for the Lorentz force. In this paper, we prove he exist enc e of global strong solution of the three dimensional magneto hydrodynamics equation under suitable initial and boundary conditions.
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