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M. Bukal, A. Jüngel, D. Matthes:
"A multidimensional nonlinear sixth-order quantum diffusion equation";
in: "ASC Report 12/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9, 1 - 35.

This paper is concerned with the analysis of a sixth-order nonlinear parabolic
equation whose solutions describe the evolution of the particle density in a quantum fluid.
We prove the global-in-time existence of weak nonnegative solutions in two and three space
dimensions under periodic boundary conditions. Moreover, we show that these solutions
are smooth and classical whenever the particle density is strictly positive, and we prove the
long-time convergence to the spatial homogeneous equilibrium at a universal exponential
rate. Our analysis strongly uses the Lyapunov property of the entropy functional.

http://www.asc.tuwien.ac.at/preprint/2011/asc12x2011.pdf