The viscous model of quantum hydrodynamics in several dimensions

Li Chen, Michael Dreher

Research output: Contribution to journalArticle

23 Citations (Scopus)

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 to the thermal equilibrium state in one, two, and three 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. Finally, we prove the global existence in a one-dimensional setting under additional assumptions.

Original languageEnglish
Pages (from-to)1065-1093
Number of pages29
JournalMathematical Models and Methods in Applied Sciences
Volume17
Issue number7
DOIs
Publication statusPublished - Jul 2007

Keywords

  • quantum hydrodynamics
  • exponential decay
  • entropy dissipation method
  • local and global existence of solutions
  • EXPONENTIAL DECAY
  • EQUATIONS
  • SYSTEMS

Cite this