  The dispersion of inertial particles continuously emitted from a point source
is analytically investigated in the limit of small inertia. Our focus is on the
evolution equation of the particle joint probability density function p(x,v,t),
x and v being the particle position and velocity, respectively. For finite
inertia, position and velocity variables are coupled, with the result that
p(x,v,t) can be determined by solving a partial differential equation in a
2d-dimensional space, d being the physical-space dimensionality. For small
inertia, (x,v)-variables decouple and the determination of p(x,v,t) is reduced
to solve a system of two standard forced advection-diffusion equations in the
space variable x. The latter equations are derived here from first principles,
i.e. from the well-known Lagrangian evolution equations for position and
particle velocity.
