The viscous model of quantum hydrodynamics
in several dimensions
L. Chen and M. Dreher
Abstract.
We investigate the viscous model of quantum hydrodynamics in one and
higher space dimensions. Exploiting the entropy dissipation method, we
prove the exponential decay of global solutions to the thermal equilibrium state in
1,2, and 3 dimensions, provided that the domain is a box. Further, we
show the local in time existence of a solution in the one dimensional
case; and in the case of higher dimensions under the assumption of
periodic boundary conditions. For a special one-dimensional setting, we can
even prove the global existence of the solution.
Math. Mod. Meth. Appl. Sci.
Vol. 17, No. 7
(2007), 1065-1093.
A preliminary version of the paper is available here:
pdf.
