Ideal magnetohydrodynamic momentum equation ($\rho D_t\mathbf{u}=-\nabla p-\rho \nabla \Phi +(\nabla \times \mathbf{B})\times \mathbf{B}/{\mu }_0$)

The inviscid magnetohydrodynamic momentum equation balances inertia, pressure, gravitational acceleration and Lorentz force density. The magnetic force separates into magnetic tension and magnetic pressure. It is coupled to the continuity equation and the ideal magnetohydrodynamic induction equation.