The fluid flow with zero material derivative of its density:

(1)	$\begin{array}{l}\displaystyle \frac{D \rho}{ Dt} = \frac{\partial \rho}{\partial t} + \rho \cdot \nabla {\bf u} = 0\end{array}$

(2)	$\begin{array}{l}\displaystyle \frac{\partial \rho}{\partial t} + \nabla (\rho \, {\bf u}) = 0\end{array}$

the Incompressible flow criteria simplifies to:

(3)	$\begin{array}{l}\displaystyle \nabla {\bf u} = 0\end{array}$

It does not necessarily means that the fluid itself is incompressible.

In many practical applications condition (3) is met for compressible fluids and the fluid flow behaves as Incompressible flow.

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