Geodesic
A Note on Regularity Criteria in Terms of Pressure for the 3D Viscous MHD Equations
Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 526-531

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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 $\pi$ belongs to $L^2(0,T,\dot B_{\infty,\infty}^{-1}(\mathbb R^3))$ or the gradient field of pressure $\nabla\pi$ belongs to $L^{2/3}(0,T,\mathrm{BMO}(\mathbb R^3))$, then the corresponding weak solution $(u,b)$ remains smooth on $[0,T]$.
Keywords: MHD equations, regularity criteria, critical Besov space. 
@article{MZM_2017_102_4_a4,
     author = {S. Gala and M. A. Ragusa},
     title = {A {Note} on {Regularity} {Criteria} in {Terms} of {Pressure} for the {3D} {Viscous} {MHD} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {526--531},
     publisher = {mathdoc},
     volume = {102},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a4/}
}
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S. Gala; M. A. Ragusa. A Note on Regularity Criteria in Terms of Pressure for the 3D Viscous MHD Equations. Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 526-531. http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a4/