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 $\pi$ 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 $[0,T]$.
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