The incompressible Navier–Stokes equations are the partial differential equations given by
where  is the velocity of the fluid,  the pressure,  the viscosity and  the external volumetric force.
By applying the Leray projection to the first equation, we may rewrite the Navier-Stokes equations as an abstract differential equation on an infinite dimensional phase space, such as , the space of continuous functions from  to  where  and  is the space of square-integrable functions on the physical domain :
where we have defined the Stokes operator  and the bilinear form  by 
The pressure and the divergence free condition are "projected away". In general, we assume for simplicity that  is divergence free, so that ; this can always be done, by adding the term  to the pressure.