Hydrodynamic approximation of the space-charge problem in terms of the charge density, $rho$, and the velocity field, $v$

The spacecharge problem is considered in the hydrodynamic approximation. The problem is formulated in terms of the chargedensity, $\rho$, and the vector velocity field, $v$, (the $\rho v$ statement). In contrast to the $Dv$ statement, the ρv statement can be used for asymmetric chargedensity distributions. A formal solution to a boundary value problem is described and its properties are considered.