The linearity of the Stokes equations in the case of an incompressible Newtonian fluid means that a Greens function, , exists.  The Greens function is found by solving the Stokes equations with the forcing term replaced by a point force acting at the origin, and boundary conditions vanishing at infinity:
where  is the Dirac delta function, and  represents a point force acting at the origin. The solution for the pressure p and velocity u with |u| and p vanishing at infinity is given by
where
is a second-rank tensor (or more accurately tensor field) known as the Oseen tensor (after Carl Wilhelm Oseen). Here, r r is a quantity such that .
The terms Stokeslet and point-force solution are used to describe . Analogous to the point charge in electrostatics, the Stokeslet is force-free everywhere except at the origin, where it contains a force of strength .
For a continuous-force distribution (density)  the solution (again vanishing at infinity) can then be constructed by superposition:
This integral representation of the velocity can be viewed as a reduction in dimensionality: from the three-dimensional partial differential equation to a two-dimensional integral equation for unknown densities.