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In this paper, we consider the Cauchy problem of the incompressible MHD system with discontinuous initial density in R³. We establish the global well-posedness of the MHD system if the initial data satisfies (ρ₀, u₀, H₀) ∈ L^∞ (R³) × Hˢ (R³) × Hˢ (R³) with 12 0 which only depends on ρ, ρ. As a byproduct, we also get the decay estimate of the solution.
Chen et al. (Wed,) studied this question.