New Regularity Criteria for Weak Solutions to the MHD Equations in Terms of an Associated Pressure

We prove that if $0<T_0<T\le \mathrm{\infty }$, $(\mathbf{u},\mathbf{b},p)$ is a suitable weak solution of the MHD equations in ${\mathbb{R}}^3\times (0,T)$ and either $$\mathcal{F}${\gamma}(p-)\in L^{\infty}(0,T_0;, L^{3/2}($\mathbb{R}$^3))$or$$\mathcal{F}${\gamma}((|$\mathbf{u}$|^2+ |$\mathbf{b}$|^2+2p)+)\in L^{\infty}(0,T_0;, L^{3/2}($\mathbb{R}$^3))$forsome$\gamma>0$,where$$\mathcal{F}$_{\gamma}(s)=s, [\ln{}(1+ s)]^{1+\gamma}$ and the subscripts “$-$” and “$+$” denote the negative and the nonnegative part, respectively, then the solution $(\mathbf{u},\mathbf{b},p)$ has no singular points in ${\mathbb{R}}^3\times (0,T_0]$.