Kinetic magnetohydrodynamic momentum equation ($\rho D_t\mathbf{u}=-\nabla \cdot \mathbf{P}+(\nabla \times \mathbf{B})\times \mathbf{B}/(4\pi )$)

In Gaussian units, the equation in the title uses the gyrotropic pressure tensor $\mathbf{P}=p_{\perp }\mathbf{I}+(p_{\parallel }-p_{\perp })\mathbf{bb}$. This allows pressure anisotropy. Its magnetic force contains both magnetic pressure and magnetic tension.