On a Steady-State Quantum Hydrodynamic Model for
By: Bo Zhang and Joseph W. Jerome
A third order quantum perturbation of the stress tensor, and a
to represent averaged collisions, are employed as perturbations
of the isentropic model for a collisionless plasma. The model is
the sense that the electric field, which forms a forcing term in the
momentum equation, is determined by the coupled Poisson equation.
As formulated, the model is a reduced version of the quantum hydrodynamic
model for semiconductors.
Existence is demonstrated for
the model, which is shown to be equivalent to a non-standard
equation. An unusual boundary condition, with the important physical
interpretation of specifying the quantum potential at the (current)
inflow boundary, is identified as essential for the theory.
This paper appeared in Nonlinear Analysis 26 (1996), 845--856.
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