MHD Fluid

$$\rho \left({\frac {Du}{Dt}}\right)=-\nabla P+J\times B+\eta \nabla ^{2}u$$

$${\frac {\partial B}{\partial t}}=\nabla \times (u\times B-\eta \nabla B)$$

$$E+u\times B=\eta J$$

$$\rho \left({\frac {D\varepsilon }{Dt}}\right)=-P\nabla \cdot u+\nabla \cdot (k\nabla T)+\eta J^{2}$$

$${\frac {D\rho }{Dt}}+\rho \nabla \cdot u=0$$