A regularity criterion of 3D incompressible MHD system with mixed pressure-velocity-magnetic field

This work focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed pressure-velocity-magnetic field in view of Lorentz spaces. Our main result shows the weak solution is regular, provided that $${\frac{\pi }{{(e^{-{\mid x\mid }^2}+\mid u\mid +\mid b\mid )}^{\theta }}\in L}^p(0,T;L^{q,\mathrm{\infty }}({\mathbb{R}}^3)),\text{ where }\frac{2}{p}+\frac{3}{}0\le \theta \le 1.$$