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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Original Russian Text © S. Gala, M. A. Ragusa, 2017, published in Matematicheskie Zametki, 2017, Vol. 102, No. 4, pp. 526–531.
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Gala, S., Ragusa, M.A. A note on regularity criteria in terms of pressure for the 3D viscous MHD equations. Math Notes 102, 475–479 (2017). https://doi.org/10.1134/S000143461709019X
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DOI: https://doi.org/10.1134/S000143461709019X