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Global-in-time existence of solutions for incompressible magnetohydrodynamic fluid equations in a bounded domain Ω ⊂ R3 with the boundary slip conditions is proved. The proof is based on the potential method. The existence is proved in a class of functions such that the velocity and the magnetic field belong to W 2,1 p (Ω × (0, T )) and the pressure q satisfies ∇q ∈ Lp(Ω × (0, T )) for p ≥ 7/3.

Global existence of solutions for incompressible magnetohydrodynamic equations