The matter which density is not dependant on pressure or temperature :

\rho(p, T) = \rho_0 = {\rm const}

which is equivalent to zero compressibility:

 c(p) \equiv 0 \Leftrightarrow  \frac{d \rho}{ dp} = 0

This also implies that material balance equation:

\frac{\partial \rho}{\partial t} + \nabla (\rho \, {\bf u}) = 0

simplifies to:

 \nabla {\bf u} = 0

The incompressible matter does not exist but in many practical applications the pressure and temperature variations stay within the sufficiently narrow range where a given matter can be considered as incompressible.

See also