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, ˙B−1 ∞,∞(R3)) or the gradient field of pressure ∇π belongs to L2/3(0, T,BMO(R3)), then the corresponding weak solution (u, b) remains smooth on [0, T ].
A Note on Regularity Criteria in Terms of Pressure for the 3D Viscous MHD Equations
Maria Alessandra, Ragusa;
2017-01-01
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 L2(0, T, ˙B−1 ∞,∞(R3)) or the gradient field of pressure ∇π belongs to L2/3(0, T,BMO(R3)), then the corresponding weak solution (u, b) remains smooth on [0, T ].File in questo prodotto:
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