Incompressible condition

The continuity equation can be written

$$\frac{\partial \rho}{\partial t} + \rho \nabla \cdot \mathbf{u}+\mathbf{u} \cdot \nabla \rho = 0,$$ (368)

which can be further written

$$\Rightarrow \frac{d \rho}{d t} = - \rho \nabla \cdot \mathbf{u}.$$ (369)

Then the incompressible condition $d \rho / d t = 0$ reduces to that

$$\nabla \cdot \mathbf{u}= 0$$ (370)

On the other hand, equation (15) indicates that

$$\frac{d \rho}{d t} = \frac{1}{\gamma} \frac{\rho}{p} \frac{d p}{d t},$$ (371)

which indicates that for incompressible plasma $d p / d t = 0$.