The transient equations of viscous quantum hydrodynamics
M. Dreher
Abstract.
We study the viscous model of quantum hydrodynamics in a bounded
domain of space dimension 1, 2, or 3. This model is a mixed order
partial differential system with nonlocal and nonlinear terms for the
particle density, current density and electric potential. By a
viscous regularization approach, we show existence and uniqueness of
local in time solutions. We propose a reformulation as an equation of
Schrödinger type, and we prove the inviscid limit.
Math. Meth. Appl. Sci.
31
(2008),
391-414.
A preliminary version of the paper is available here:
pdf.
