Editing Navier–Stokes equations (section)

===Continuity equation for incompressible fluid===
{{Main|Continuity equation}}

Regardless of the flow assumptions, a statement of the [[conservation of mass]] is generally necessary. This is achieved through the mass [[continuity equation]], as discussed above in the "General continuum equations" within this article, as follows:
<math display="block">
\begin{align}
\frac{\mathbf{D}m}{{\mathbf{Dt}}}&={\iiint\limits_V}({\frac{\mathbf{D}\rho}{{\mathbf{Dt}}} + \rho (\nabla \cdot \mathbf{u})})dV \\
\frac{\mathbf{D}\rho}{{\mathbf{Dt}}} + \rho (\nabla \cdot{\mathbf{u}})&=\frac{\partial\rho}{\partial t} + ({\nabla \rho}) \cdot{\mathbf{u}} + {\rho}(\nabla \cdot \mathbf{u})= \frac{\partial\rho}{\partial t} + \nabla\cdot({\rho \mathbf{u}})= 0 
\end{align}</math>
A fluid media for which the [[density]] (<math>\rho</math>) is constant is called [[Incompressible flow|''incompressible'']]. Therefore, the rate of change of [[density]] (<math>\rho</math>) with respect to time <math>(\frac{\partial\rho}{\partial t})</math> and the [[gradient]] of density <math>(\nabla \rho)</math> are equal to zero <math>(0)</math>. In this case the general equation of continuity, <math>\frac{\partial\rho}{\partial t} + \nabla\cdot({\rho \mathbf{u}})= 0</math>, reduces to:  <math>\rho(\nabla{\cdot}{\mathbf{u}}) = 0</math>. Furthermore, assuming that [[density]] (<math>\rho</math>) is a non-zero constant <math>(\rho \neq 0)</math> means that the right-hand side of the equation <math>(0)</math> is divisible by [[density]] (<math>\rho</math>). Therefore, the continuity equation for an [[Incompressible flow|incompressible fluid]] reduces further to:<big><math display="block">(\nabla{\cdot{\mathbf{u}}}) = 0</math></big>This relationship,  <small><math display="inline">(\nabla{\cdot{\mathbf{u}}}) = 0</math></small>,  identifies that the [[divergence]] of the flow velocity [[Vector field|vector]] (<math>\mathbf{u}</math>) is equal to zero <math>(0)</math>, which means that for an [[Incompressible flow|incompressible fluid]] the [[Flow velocity|flow velocity field]] is a [[solenoidal vector field]] or a [[Divergence-free|divergence-free vector field]]. Note that this relationship can be expanded upon due to its uniqueness with the [[vector Laplace operator]] <math>(\nabla ^{2} \mathbf{u} =\nabla (\nabla \cdot \mathbf{u} )-\nabla \times (\nabla \times \mathbf{u} ))</math>, and [[vorticity]] <math>(\vec \omega = \nabla \times \mathbf{u})</math> which is now expressed like so, for an   [[Incompressible flow|incompressible fluid]]:<math display="block">\nabla ^{2}\mathbf {u} = - (\nabla \times (\nabla \times \mathbf {u} )) = - (\nabla \times \vec \omega)</math>