A note on regularity criteria in terms of pressure for the 3D viscous MHD equations

Аннотация

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 L₂(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].