Abstract
This note is devoted to the study of the smoothness of weak solutions to the Cauchy problem for three-dimensional magneto-hydrodynamic system in terms of the pressure. It is proved that if the pressure π belongs to L 2(0, T, Ḃ ∞,∞ −1 (ℝ3)) or the gradient field of pressure ∇π belongs to L 2/3(0, T, BMO(ℝ3)), then the corresponding weak solution (u, b) remains smooth on [0, T].
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